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【332442】3.3 圆周角 专项练习1

时间:2025-01-21 12:47:19 作者: 字数:3723字
简介:

圆心角和圆周角

随堂检测

1.如图,图中圆周角的个数是( )

组合 13 A9 B12 C8 D14









2.如图,圆∠BOC=100 o,则圆周角∠BAC( )

A100 o B130 o C50 o D80o

3.如图,AB为⊙O的直径,点CQO上,∠B=50 o,则∠A等于( )

A80 o B60 o C50 o D40 o

4如图,点ABC都在⊙O上,连结ABBCACOAOB,且∠BAO=25o,则∠ACB的大小为___________

5如图,等腰三角形ABC的底边BC的长为a,以腰AB为直径的⊙OBC于点D.则BD的长为___________

组合 22






典例分析

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 图,已知在⊙O中,直径AB10cm,弦AC6cm,∠ACB的平分线交⊙OD,求BCADBD的长.





分析:所要求的三线段BCADBD的长,能否把这三条线段转化为是直角三角形的直角边问题,由于已知AB为⊙O的直径,可以得到△ABC和△ADB都是直角三角形,又因为CD平分∠ACB,所以可得  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> =  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> ,可以得到弦AD=DB,这时由勾股定理可得到三条线段BCADDB的长.

解:AB为直径,∴∠ACB=∠ADB=90°

Rt△ABC中, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

CD平分∠ACB

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> =  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

在等腰直角三角形ADB中,

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

点评:利用“直径所对的圆周角是直角”构造直角三角形解题.

课下作业

拓展提高

1如图.⊙OOA⊥BC,∠CDA=25o,则∠AOB的度数为_______

2如图.AB为⊙O的直径,点CD在⊙O上,∠BAC=50 o.则∠ADC=_______

组合 29







3如图,AB是半圆O的直径,∠BAC=30 oDAC上任意一点,那么∠D的度数是 ( )

A150 o B120 o C100 o D90 o

4 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> .如图,∆ABC内接于⊙OAD是⊙O的直径,∠ABC=30o,则∠CAD等于( )

A30 o B40 o

C50 o D60 o



5.如图,∠APC=∠CPB=60 o,请推测△ABC是什么三角形,并证明猜想的正确性.

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>






6如图ADABC的高AEABC的外接圆的直径试说明AB·AC=AE·AD

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>







7 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 如图,点ABC为圆O上的三个点,∠AOB= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> ∠BOC, ∠BAC=45 o,求∠ACB的度数.











8 如图,AB是⊙O的直径,C是⊙O上一点,连结AC,过点C作直线CD⊥AB,垂足为点D(AD<DB),点EDB上任意一点(DB除外),直线CE交⊙O于点F,连结AF,与直线CD交于点G

(1)试说明AC2=AG·AF

(2)若点EAD(AD除外)上任意一点,上述结论是否仍然成立?若成立.请画出图形,并给予证明;若不成立,请说明理由.

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>






体验中考

1(温州)如图,∠AOB是⊙0的圆心角,∠AOB=80°,则弧 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 所对圆周角∠ACB的度数是( )

A40° B45° C50° D80°

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

2(凉山州)如图, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 的外接圆,已知 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> ,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 的大小为( )

A40° B30° C45° D50°

3(山西省)如图所示, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 是圆上的点, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 度.

4 (宁夏)已知:如图, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 的直径, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 于点 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 于点 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

( <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 1) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a> 的度数;

(2)求证: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>



参考答案

随堂检测

1B 提示:利用弧来找圆周角

2C 提示 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

3D 提示: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

4650 提示: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

5 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

课下作业

拓展提高

1500 提示: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

2 400 提示:连接BC <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

3B 提示:连接BC

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

4D

5 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

6 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>



7 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

8(1)证明: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

体验中考

1A 提示: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

2A

3300 提示: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>

4 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/948/" title="圆周角" class="c1" target="_blank">圆周角</a> <a href="/tags/1254/" title="圆周" class="c1" target="_blank">圆周</a>