1 . 如图所示,在⊙O中,相交于点E的两弦AB,CD的中点分别是M,N,直线MO与直线CD相交于点F.证明
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/cdcc2cdf-e541-42c8-bbce-48c05d3a473d.png?resizew=240)
(1)∠MEN+∠NOM=180°;
(2)FE·FN=FM·FO.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/cdcc2cdf-e541-42c8-bbce-48c05d3a473d.png?resizew=240)
(1)∠MEN+∠NOM=180°;
(2)FE·FN=FM·FO.
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2 . 如图所示,PA与圆O相切于点A,不过圆心O的割线PCB与直径AE相交于D点.已知∠BPA=30°,AD=2,PC=1,则圆O的半径等于________ .
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758200027602944/1817081830203392/STEM/91b436abd3534b12b4bbcc4893490293.png?resizew=87)
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3 . 如图所示,AB是半圆O的直径,点C在半圆上,CD⊥AB于点D,且AD=3DB,设∠COD=θ,则tan2
=__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16d92d3ccdf0ecfaa43eb8ed62ae5a4.png)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758200027602944/1817081830195200/STEM/027e6e38fed14b0d94131d2fd983e44c.png?resizew=107)
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4 . 如图所示,⊙O是△ABC的外接圆,AD是⊙O的直径,连接CD,若⊙O的半径r=
,AC=2,则cos B的值是( )
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758200027602944/1817081830154240/STEM/c15e7f13ca2b468897843317de4c17b0.png?resizew=84)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758200027602944/1817081830154240/STEM/c15e7f13ca2b468897843317de4c17b0.png?resizew=84)
A.![]() | B.![]() |
C.![]() | D.![]() |
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13-14高二·全国·课后作业
5 . 如图所示,已知⊙O的半径为5,两弦AB、CD相交于AB的中点E,且AB=8,CE∶ED=4∶9,则圆心到弦CD的距离为
![](https://img.xkw.com/dksih/QBM/2014/3/25/1571575004364800/1571575009558528/STEM/4227f57634a04273b68fcbb7a0d43dfa.png)
![](https://img.xkw.com/dksih/QBM/2014/3/25/1571575004364800/1571575009558528/STEM/4227f57634a04273b68fcbb7a0d43dfa.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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13-14高二·全国·课后作业
6 . 如图所示,四边形ABCD是⊙O的内接四边形,延长BC到E,已知∠BCD∶∠ECD=3∶2,那么∠BOD等于
![](https://img.xkw.com/dksih/QBM/2014/3/25/1571575323123712/1571575328088064/STEM/afa16a05f8004ce4a6b9850f31f6b919.png)
![](https://img.xkw.com/dksih/QBM/2014/3/25/1571575323123712/1571575328088064/STEM/afa16a05f8004ce4a6b9850f31f6b919.png)
A.120° | B.136° |
C.144° | D.150° |
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13-14高二·全国·课后作业
7 . 如图所示,P、Q分别在BC和AC上,BP∶CP=2∶5,CQ∶QA=3∶4,则
( ).
![](https://img.xkw.com/dksih/QBM/2014/8/6/1571833331859456/1571833337487360/STEM/0980595d6a6f4378a0e0dcc854488ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c3aea74102ef08bdd93016c249b7b0.png)
![](https://img.xkw.com/dksih/QBM/2014/8/6/1571833331859456/1571833337487360/STEM/0980595d6a6f4378a0e0dcc854488ed3.png)
A.3∶14 | B.14∶3 | C.17∶3 | D.17∶14 |
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