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【332441】3.3 圆周角 同步练习

时间:2025-01-21 12:47:08 作者: 字数:2148字
简介:

圆周角

一、选择题

1.如图1ABC三点在⊙O上,∠AOC=100°,则∠ABC等于( ).

A140° B110° C120° D130°

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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/50/" title="同步" class="c1" target="_blank">同步</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/50/" title="同步" class="c1" target="_blank">同步</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) (2) (3)

2.如图2,∠1、∠2、∠3、∠4的大小关系是( )

A.∠4<∠1<∠2<∠3 B.∠4<∠1=∠3<∠2

C.∠4<∠1<∠3∠2 D.∠4<∠1<∠3=∠2

3.如图3AD是⊙O的直径,AC是弦,OB⊥AD,若OB=5,且∠CAD=30°,则BC等于( ).

A3 B3+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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> C5- <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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/50/" title="同步" class="c1" target="_blank">同步</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> D5

二、填空题

1.半径为2a的⊙O中,弦AB的长为2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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,则弦AB所对的圆周角的度数是________

2.如图4AB是⊙O的直径,CDE都是圆上的点,则∠1+∠2=_______

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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/50/" title="同步" class="c1" target="_blank">同步</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) (5)

3.如图5,已知△ABC为⊙O内接三角形,BC=1∠A=60°则⊙O半径为_______

三、综合提高题

1.如图,弦AB把圆周分成12的两部分,已知⊙O半径为1,求弦长AB

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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.如图,已知AB=AC,∠APC=60°

1)求证:△ABC是等边三角形.

2)若BC=4cm,求⊙O的面积.

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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>



3.如图,⊙C经过坐标原点,且与两坐标轴分别交于点A与点B,点A的坐标为(04),M是圆上一点,∠BMO=120°

1)求证:AB为⊙C直径.

2)求⊙C的半径及圆心C的坐标.

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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

一、1D 2B 3D

二、1120°60° 290° 3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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>

三、1 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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.(1)证明:∵∠ABC=∠APC=60°

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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> ,∴∠ACB=∠ABC=60°,∴△ABC为等边三角形.

2)解:连接OC,过点OOD⊥BC,垂足为D

Rt△ODC中,DC=2,∠OCD=30°

OD=x,则OC=2x,∴4x2-x2=4,∴OC= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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/50/" title="同步" class="c1" target="_blank">同步</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>

3.(1)略 (24,(-2  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</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