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【327824】2023年湖南省衡阳市中考数学真题

时间:2025-01-20 20:22:55 作者: 字数:20480字
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2023年湖南省衡阳市中考数学真题

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得分




一、选择题

1.中国是最早采用正负数表示相反意义的量、并进行负数运算的国家.若收入500元记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 元,则支出237元记作(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
0
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

2.下列长度的各组线段能组成一个三角形的是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

3.下面四种化学仪器的示意图是轴对称图形的是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>         

4.作为中国非物质文化遗产之一的紫砂壶,成型工艺特别,造型式样丰富,陶器色泽古朴典雅,从一个方面鲜明地反映了中华民族造型审美意识.如图是一把做工精湛的紫砂壶“景舟石瓢”,下面四幅图是从左面看到的图形的是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

5.计算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的结果正确的是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

6.据共青团中央202353日发布的中国共青团团内统计公报,截至202212月底,全国共有共青团员7358万.数据7358万用科学记数法表示为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

7.对于二次根式的乘法运算,一般地,有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> .该运算法则成立的条件是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

8.如图,在四边形ABCD中,BCAD,添加下列条件,不能判定四边形ABCD是平行四边形的是(  )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
A
ABCD
BABCD
C.∠A=∠C
DBCAD

9.《孙子算经》中有“鸡兔同笼”问题:“今有鸡兔同笼,上有三十五头,下有九十四足,问鸡兔各几何.”设有x只鸡,y只兔.依题意,可列方程组为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

10.某射击运动队进行了五次射击测试,甲、乙两名选手的测试成绩如下表.甲、乙两名选手成绩的方差分别记为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的大小关系是(       

测试次数

1

2

3

4

5

5

10

9

3

8

8

6

8

6

7


A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
.无法确定

11.我们可以用以下推理来证明“在一个三角形中,至少有一个内角小于或等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ”.假设三角形没有一个内角小于或等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即三个内角都大于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> .则三角形的三个内角的和大于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,这与“三角形的内角和等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ”这个定理矛盾.所以在一个三角形中,至少有一个内角小于或等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> .上述推理使用的证明方法是(       
A
.反证法
B
.比较法
C
.综合法
D
.分析法

12.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,若关于x的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> .关于x的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> .则下列结论正确的是(        
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

评卷人

得分




二、填空题

13.在平面直角坐标系中,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 所在象限是第________象限.

14.一个布袋中放着3个红球和9个黑球,这两种球除了颜色以外没有任何其他区别.布袋中的球已经搅匀.从布袋中任取1个球,取出红球的概率是________

15.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,则代数式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的值为________

16.已知关于x的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的一个根是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,则它的另一个根是________

17.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> .以点C为圆心,r为半径作圆,当所作的圆与斜边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 所在的直线相切时,r的值为________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    

18.如图,用若干个全等的正五边形排成圆环状,图中所示的是其中3个正五边形的位置.要完成这一圆环排列,共需要正五边形的个数是________ 个.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    

评卷人

得分




三、解答题

19.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

20.解不等式组: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

21.2023327日是第28个全国中小学生安全教育日,为提高学生安全防范意识和自我防护能力,某学校举行了校园安全知识竞赛活动.现从八、九年级中各随机抽取15名学生的竞赛成绩(百分制)进行整理、描述和分析(成绩得分用x表示,80分及以上为优秀,共分成四组,A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ),并给出下面部分信息:
八年级抽取的学生竞赛成绩在C组中的数据为:848488
九年级抽取的学生竞赛成绩为:687775100801008286959110086849487
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
八、九年级抽取的学生竞赛成绩统计表

年级

平均数

中位数

众数

优秀率

87

a

98

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

87

86

b

c

根据以上信息,解答下列问题:
(1)
填空: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ________ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ________ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ________
(2)
该校八、九年级共500人参加了此次竞赛活动,请你估计该校八、九年级参加此次竞赛活动成绩达到90分及以上的学生人数.

22.如图,正比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的图象与反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的图象相交于点A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
(1)求点A的坐标.
(2)
分别以点OA为圆心,大于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 一半的长为半径作圆弧,两弧相交于点B和点C,作直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,交x轴于点D.求线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的长.

23.随着科技的发展,无人机已广泛应用于生产生活,如代替人们在高空测量距离和高度.圆圆要测量教学楼 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的高度,借助无人机设计了如下测量方案:如图,圆圆在离教学楼底部 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米的C处,遥控无人机旋停在点C的正上方的点D处,测得教学楼 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的顶部B处的俯角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米.已知目高 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
(1)求教学楼 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的高度.
(2)
若无人机保持现有高度沿平行于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的方向,以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> /秒的速度继续向前匀速飞行,求经过多少秒时,无人机刚好离开圆圆的视线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

24.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的直径, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是一条弦,D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的中点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点E,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点F,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点H <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点G
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
(1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的半径.

25.1[问题探究]
如图1,在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 中,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 相交于点O.在线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 上任取一点P(端点除外),连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
将线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 绕点P逆时针旋转,使点D落在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的延长线上的点Q处.当点P在线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 上的位置发生变化时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的大小是否发生变化?请说明理由;
探究 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的数量关系,并说明理由.
2[迁移探究]
如图2,将正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 换成菱形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,其他条件不变.试探究 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的数量关系,并说明理由.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    

26.如图,已知抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> x轴交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 和点B,与y轴交于点C,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,过BC两点作直线.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
(1)a的值.
(2)
将直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 向下平移 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 个单位长度,交抛物线于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 两点.在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 上方的抛物线上是否存在定点D,无论m取何值时,都是点D到直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的距离最大,若存在,请求出点D的坐标;若不存在,请说明理由.
(3)
抛物线上是否存在点P,使 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,若存在,请求出直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式;若不存在,请说明理由.

参考答案

1.B

【解析】
根据相反意义的量的意义解答即可.
收入500元记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 元,
支出237元记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 元,
故选B

2.D

【解析】
根据两边之和大于第三边,两边之差小于第三边判断即可.
A.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,不符合题意;
B.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,不符合题意;
C.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,不符合题意;       
D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,符合题意,
故选D

3.C

【解析】
根据轴对称图形的概念对各选项分析判断即可得解.
解:A.不是轴对称图形,故本选项不合题意;
B
.不是轴对称图形,故本选项不符合题意;
C
.是轴对称图形,故本选项合题意;
D
.不是轴对称图形,故本选项不合题意.
故选:C

4.B

【解析】
根据左视图定义从左向右看得到的图形,从左面看看到壶嘴,画的全身,看不见弧把手,对各选项进行分析判断即可.
A.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是从上向下看得到的图形为俯视图,故选项A不合题意;
B.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是从左向右看得到的图形为左视图,故选项B符合题意;
C.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是从下往上看得到的图形是仰视图,故选项C不合题意;
D.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是从前往后看得到的图形是主视图,故选项D不合题意.
故选择B

5.B

【解析】
运用积的乘方法则、幂的乘方法则即可得出结果.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故选:B

6.A

【解析】
科学记数法的表示形式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的形式,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 为整数.确定 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的值时,要看把原数变成 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 时,小数点移动了多少位, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的绝对值与小数点移动的位数相同.当原数绝对值 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是正数;当原数的绝对值 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是负数.据此可得出结果.
7358
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故选:A

7.D

【解析】
根据二次根式有意义的条件得出不等式组,再解不等式组即可得出结果.
解:根据二次根式有意义的条件,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故选:D

8.A

【解析】
依据平行四边形的判定,依次分析判断即可得出结果.
解:A、当BCADABCD时,不能判定四边形ABCD是平行四边形,故此选项符合题意;
B
、当ABCDBCAD时,依据两组对边分别平行的四边形是平行四边形,能判定四边形ABCD是平行四边形,故此选项不合题意;
C
、当BCAD,∠A=∠C时,可推出ABDC,依据两组对边分别平行的四边形是平行四边形,能判定四边形ABCD是平行四边形,故此选项不合题意;
D
、当BCADBCAD时,依据一组对边平行且相等的四边形是平行四边形,能判定四边形ABCD是平行四边形,故此选项不合题意;
故选:A

9.C

【解析】
根据等量关系“鸡的只数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 兔的只数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ”和“2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 鸡的只数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 兔的只数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ”即可列出方程组.
解:设有x只鸡,y只兔,
由题意可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故选:C

10.A

【解析】
先分别求出甲、乙的平均数,再求出甲、乙的方差即可得出答案.
解:甲的平均数为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
甲的方差为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
乙的平均数为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
乙的方差为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故选:A

11.A

【解析】
根据反证法的步骤分析判断,即可解答.
解:假设三角形没有一个内角小于或等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即三个内角都大于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
则三角形的三个内角的和大于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
这与“三角形的内角和等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ”这个定理矛盾.
所以在一个三角形中,至少有一个内角小于或等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
以上步骤符合反证法的步骤.
故推理使用的证明方法是反证法.
故选:A

12.B

【解析】
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 看做是直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 与抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 交点的横坐标,把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 看做是直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 与抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 交点的横坐标,画出对应的函数图象即可得到答案.
解:如图所示,设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 与抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 交于AB两点,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 与抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 交于CD两点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,关于x的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,关于x的方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 分别是ABCD的横坐标,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故选B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    

13.

【解析】
根据各象限内点的坐标特征解答.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的横坐标为负数,纵坐标为负数,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 在第三象限,
故答案为:三.

14. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ##0.25

【解析】
根据公式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 计算即可.
一个布袋中放着3个红球和9个黑球,
取出红球的概率是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

【解析】
先通分,再根据同分母分式的减法运算法则计算,然后代入数值即可.
解:原式= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

16.5

【解析】
根据一元二次方程根与系数的关系可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,根据该方程一个根为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即可求出另一个根.
解:根据题意可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
该方程一个根为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,令 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故答案为:5

17. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

【解析】
根据勾股定理,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,根据切线的性质,得到圆的半径等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 边上的高,根据直角三角形的面积不变性计算即可.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
根据切线的性质,得到圆的半径等于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 边上的高,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

18.10

【解析】
先求出正五边形的外角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,进而得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即可求解.
解:根据题意可得:
正五边形的一个外角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
共需要正五边形的个数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> (个),
故答案为:10
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    

19. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

【解析】
根据求一个数的绝对值,二次根式的性质,有理数的乘法进行计算即可求解.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

20. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

【解析】
分别求出每一个不等式的解集,根据口诀:同大取大、同小取小、大小小大中间找、大大小小找不到确定不等式组的解集.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
解不等式①得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
解不等式②得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
不等式组的解集为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

21.(1)84100 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
(2)200


【解析】
1)根据中位数的定义得出a为排序后第八名学生的成绩;找出抽取的九年级学生的竞赛成绩中出现次数最多的分数,即可求出b;用抽取的九年级学生的竞赛成绩中80分以上的个数除以15,即可求出c
2)用500人乘以抽取的八、九年级学生竞赛成绩中90分以上的人数所占百分比,即可求解.
1)解:∵一共抽取八年级学生15人,
中位数是排序后的第8个数据,
∵1+5=6

8个数据落在C组,
a第八名学生成绩,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
抽取的九年级学生竞赛成绩中,100分出现了3次,出现次数最多,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
抽取的九年级学生竞赛成绩中,80分及以上的有12个,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故答案为:84100 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
2)解:根据频数分布直方图可得,抽取的八年级学生竞赛成绩中,90分以上的有6个;
根据抽取的九年级学生的竞赛成绩可得,90分以上的有6个;
该校八、九年级参加此次竞赛活动成绩达到90分及以上的学生人数为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> (人),
答:该校八、九年级参加此次竞赛活动成绩达到90分及以上的学生人数为200人.

22.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

【解析】
1)解两个函数联立组成的方程组即可;
2)由题意可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 垂直平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,如图,根据线段垂直平分线的性质可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,根据两点间的距离建立方程,解方程即可求出答案.
1)解:解方程组 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
2)解:由题意可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 垂直平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,如图,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    

23.(1)教学楼 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的高度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
(2)
无人机刚好离开视线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的时间为12

【解析】
1)过点B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点G,根据题意可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,通过证明四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 为矩形,得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,进而得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,最后根据线段之间的和差关系可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即可求解;
2)连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 并延长,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点H,先求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,进而得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,即可求解.
1)解:过点B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点G
根据题意可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 为矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> (米),
答:教学楼 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的高度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米.
2)解:连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 并延长,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点H
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 米,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> (米),
无人机以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> /秒的速度飞行,
离开视线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的时间为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> (秒),
答:无人机刚好离开视线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的时间为12秒.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    

24.(1)见解析
(2)5

【解析】
1)根据D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的中点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点E,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 即可得证.
2)根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,运用勾股定理,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,结合 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,运用勾股定理,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,从而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 中,利用勾股定理计算x即可.
1)∵D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的直径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
2)∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的直径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> (舍去),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的半径为5

25.1)①见解析;②不变化, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,理由见解析;③ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,理由见解析;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,理由见解析

【解析】
1)①根据正方形的性质证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即可得到结论;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,垂足分别为点MN,如图,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,证明四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是矩形,推出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> , 得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,进而可得结论;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点E,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点F,如图,证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 即可得出结论;
2)先证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点G,如图,则四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是平行四边形,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 都是等边三角形,进一步即可证得结论.
1)①证明:∵四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是正方形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的大小不发生变化, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
证明:作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,垂足分别为点MN,如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是正方形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是矩形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
证明:作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点E,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点F,如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>           
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是正方形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点M
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
证明:∵四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是菱形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是等边三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 垂直平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点G,如图,
则四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是平行四边形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 都是等边三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>        
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点M,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

26.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
(2)
存在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,理由见详解
(3)
存在点P,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>

【解析】
1)根据待定系数法即可得出结果;
2)设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 轴交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 轴交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,先证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是等腰直角三角形,再表示出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的长度,根据二次函数的性质即可得出结果;
3)分两种情况讨论,当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 下方时,与当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 上方时.
1)解:抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> x轴交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
2)解:存在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,理由如下:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 轴交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,由(1)中结论 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,得抛物线的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 轴交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 是等腰直角三角形,
设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
将直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 向下平移 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 个单位长度,得直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 有最大值 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
此时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 也有最大值, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
3)解:存在点P,理由如下:
当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 下方时,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 轴上取点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,作直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 交抛物线于(异于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> )点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>    
由(2)中结论,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,代入点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 上方时,如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 轴上取点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 交抛物线于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>        
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,代入点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
故设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,且过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> ,
故设直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>
综上所述:直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a> 的解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/982/" title="湖南省" class="c1" target="_blank">湖南省</a> <a href="/tags/983/" title="衡阳" class="c1" target="_blank">衡阳</a> <a href="/tags/1121/" title="湖南" class="c1" target="_blank">湖南</a>