1 . 如图,定直线与定
相离,
为
上任意一点,
为
的两条切线,
为两切点,
其垂足为点
,
交于点
,证明:
为定长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ae16cdf6ce02a4adae05b010d59f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca65b9c5449c3ad19e136f9026b9bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://img.xkw.com/dksih/QBM/2017/9/20/1778298281328640/1779386613342208/STEM/d36624ed926e464bbdfbadbbc649ede0.png?resizew=190)
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2 . 在平面直角坐标系中,曲线
坐标轴的交点都在圆C上,
(1)求圆C的方程;
(2)如果圆C与直线
交于A,B两点,且
,求
的值.
![](https://img.xkw.com/dksih/QBM/2011/6/16/1570241138696192/1570241143767040/STEM/f4e5a37baf094cbdb6b494123957b6f6.png)
(1)求圆C的方程;
(2)如果圆C与直线
![](https://img.xkw.com/dksih/QBM/2011/6/16/1570241138696192/1570241143767040/STEM/32aeb8cfa20c4c9bb4659eebdf3f5ba3.png)
![](https://img.xkw.com/dksih/QBM/2011/6/16/1570241138696192/1570241143767040/STEM/b89e2ca6cdf04e73b0212992e49707be.png)
![](https://img.xkw.com/dksih/QBM/2011/6/16/1570241138696192/1570241143767040/STEM/01e92a2909d54312a9d555400e76a8e9.png)
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名校
3 . 如图,设
和
都是等边三角形,且
,则
的度数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4b17ce6e90cd3810a3696262e94c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e016fac9484f4f6652da209c9b85d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a55a1a244f81097e05e715b69580faa.png)
![](https://img.xkw.com/dksih/QBM/2017/8/29/1762653204406272/1765471269150720/STEM/3e1a75369a1845f480297f5f73fc72d2.png?resizew=208)
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名校
4 . 若四边形的一组对边中点的连线的长为
,另一组对边的长分别为
,
,则
与
的大小关系是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
5 . 如图,
,垂足分别为
,若
,则
的长为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5be3facae1ecc4cc1c2cb96280f92ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14af8de7575341e02ee92cd0e33312b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e493fab43e5cf7aa9675e0c40fe15fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2017/8/18/1754646343540736/1754861942030336/STEM/0dce344eb15b4d779ecf09556f41a6d2.png?resizew=118)
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真题
6 . 【选修4-1:几何证明选讲】
如图,AB为半圆O的直径,直线PC切半圆O于点C,AP⊥PC,P为垂足.
![](https://img.xkw.com/dksih/QBM/2017/8/7/1746946785624064/1747038148124672/STEM/f4e217c9aa914eff8ada98e8c8c22b1b.png?resizew=219)
求证:(1)∠PAC=∠CAB;
(2)AC2 =AP·AB
如图,AB为半圆O的直径,直线PC切半圆O于点C,AP⊥PC,P为垂足.
![](https://img.xkw.com/dksih/QBM/2017/8/7/1746946785624064/1747038148124672/STEM/f4e217c9aa914eff8ada98e8c8c22b1b.png?resizew=219)
求证:(1)∠PAC=∠CAB;
(2)AC2 =AP·AB
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7 . 已知直线
与圆![](https://img.xkw.com/dksih/QBM/2017/4/26/1674164959813632/1679890538569728/STEM/a0b14e18bbd848a39e4368439b8f3214.png?resizew=16)
相交于
两点,且线段
是圆
的所有弦中最长的一条弦,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c93c4093f63750592ad63dd781c9f3.png)
![](https://img.xkw.com/dksih/QBM/2017/4/26/1674164959813632/1679890538569728/STEM/a0b14e18bbd848a39e4368439b8f3214.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa57902cffdd4f79a787b901cd07f60b.png)
![](https://img.xkw.com/dksih/QBM/2017/4/26/1674164959813632/1679890538569728/STEM/831d489ee52f46e89c7bce885aeb0afe.png?resizew=32)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.2 | B.![]() |
C.![]() | D.1 |
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8 . 如图,PA切圆O于点A,割线PBC经过圆心O,若PB=OB=1,OD平分∠AOC,交圆O于点D,连接PD交圆O于点E,则PE的长等于( )
![](https://img.xkw.com/dksih/QBM/2017/7/8/1732926192410624/1736590201782272/STEM/8cfe286cea9147fd9d2f7753c9016565.png?resizew=159)
![](https://img.xkw.com/dksih/QBM/2017/7/8/1732926192410624/1736590201782272/STEM/8cfe286cea9147fd9d2f7753c9016565.png?resizew=159)
A.![]() ![]() | B.![]() | C.![]() | D.![]() |
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9 . 如图所示,△ABC内接于圆O,过点A的切线交BC的延长线于点P,D为AB的中点,DP交AC于点M,若BP=8,AM=4,AC=6,则PA=( )
![](https://img.xkw.com/dksih/QBM/2017/7/8/1732926192410624/1736590201765888/STEM/2a6aa2d7eb944f3ebab6cd0988002720.png?resizew=156)
![](https://img.xkw.com/dksih/QBM/2017/7/8/1732926192410624/1736590201765888/STEM/2a6aa2d7eb944f3ebab6cd0988002720.png?resizew=156)
A.4![]() | B.3![]() | C.![]() | D.5![]() |
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10 . 如图,BD⊥AE,∠C=90°,AB=4,BC=2,AD=3,则CE=( )
![](https://img.xkw.com/dksih/QBM/2017/7/8/1732926192410624/1736590201716736/STEM/0ad31bbc32664c0f889be78fe6fe353c.png?resizew=137)
![](https://img.xkw.com/dksih/QBM/2017/7/8/1732926192410624/1736590201716736/STEM/0ad31bbc32664c0f889be78fe6fe353c.png?resizew=137)
A.![]() | B.![]() | C.![]() | D.![]() |
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