1 . [选修4—1:几何证明选讲]
如图,ABCD为圆内接四边形,延长两组对边分别交于点E,F.M,N为AB,CD上两点,EM=EN,点F在MN的延长线上.求证:∠BFM=∠AFM.
如图,ABCD为圆内接四边形,延长两组对边分别交于点E,F.M,N为AB,CD上两点,EM=EN,点F在MN的延长线上.求证:∠BFM=∠AFM.
![](https://img.xkw.com/dksih/QBM/2018/5/25/1953107742081024/2007656974417920/STEM/eface4f75c1b437fb58753f845e89d4c.png?resizew=164)
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2 . (选修4-1:几何证明选讲)在圆O中,AB,CD是互相平行的两条弦,直线AE与圆O相切于点A,且与CD的延长线交于点E,求证:AD2=AB·ED.
![](https://img.xkw.com/dksih/QBM/2017/6/1/1699409391165440/1699652214628352/STEM/9743b396f71848a6950fd9e471ee5b55.png?resizew=239)
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3 . [选修41:几何证明选讲]
如图,圆
的弦
,
交于点
,且
为弧
的中点,点
在弧
上.若
,求
的度数.
如图,圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f6e483598bba7f3fafc18d8f9f1c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868ff1350bd72625328c85c3097cd85e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/26407114-1dfd-4a00-ba45-0735eb9418d8.png?resizew=142)
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2012·江苏·一模
4 . 选修4-1:几何证明选讲如图,
是直角,圆O与AP相切于点T,与AQ相交于两点B,C.求证:BT平分![](https://img.xkw.com/dksih/QBM/2012/2/7/1570719392202752/1570719397658624/STEM/e537f22ad58f478bb362aa939333f94d.png)
![](https://img.xkw.com/dksih/QBM/2012/2/7/1570719392202752/1570719397658624/STEM/abf84cec5306414086d48389a9ce3b39.png)
![](https://img.xkw.com/dksih/QBM/2012/2/7/1570719392202752/1570719397658624/STEM/e537f22ad58f478bb362aa939333f94d.png)
![](https://img.xkw.com/dksih/QBM/2012/2/7/1570719392202752/1570719397658624/STEM/538203391a604d159433b08c0f9ad1f6.png)
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2011·黑龙江哈尔滨·三模
5 . 如图,AB是半圆O的直径,C是圆周上一点(异于A,B),过C作圆O的切线
过A作直线
的垂线AD,垂足为D,AD交半圆于点E,求证:CB=CE.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee7f51b707170c7b1e85b245992144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2011/5/18/1570208444530688/1570208449798144/STEM/1bcf372c1e7e4ce09cf687c6e8114806.png?resizew=147)
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2011·广东广州·高考模拟
6 . 在梯形
中,
,
,
,点
、
分别在
、
上,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b95463a97c60db3250cb641bf6523d.png)
的长为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0facf189b2a3153beb7b9e077d3b1146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948709398d7585ff2b99a0291071bc58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b8f3a66ab29707453069ff17a88e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b95463a97c60db3250cb641bf6523d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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2011·山西·一模
7 . 选修4-1:几何证明选讲
如图,直线AB过圆心O,交圆O于A,B,直线AF交圆O于F(不与B重合),直线
与圆O相切于C,交AB于E,且与AF垂直,垂足为G,连接AC.
![](https://img.xkw.com/dksih/QBM/2011/4/23/1570127651241984/1570127656550400/STEM/1e69188872874bc9a0fabb4b879d7859.png?resizew=148)
求证:(Ⅰ)
;
(Ⅱ)
.
如图,直线AB过圆心O,交圆O于A,B,直线AF交圆O于F(不与B重合),直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2011/4/23/1570127651241984/1570127656550400/STEM/1e69188872874bc9a0fabb4b879d7859.png?resizew=148)
求证:(Ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f63ded62470f6621ff35272e95e903f.png)
(Ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed5cb81a0108ef64ccd27983895eec3.png)
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2011·广东·一模
8 . (几何证明选讲选做题)如图4,
为圆
的切线,
为切点,
,圆
的面积为
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdd62c479eb1f4907868c723048ca7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5745e2dc1d5308872c68ae932cd13ffa.png)
![](https://img.xkw.com/dksih/QBM/2011/4/7/1570110290182144/1570110295465984/STEM/25de639ae1fd40c2aec7b1fc5c490316.png?resizew=143)
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2011·广东·一模
9 . 如图,在
中,
则
线段
的取值范围为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67060552a53c4b2841042018e45adfdd.png)
线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390673ed1f32c7ced6ed818f7f683285.png)
![](https://img.xkw.com/dksih/QBM/2011/3/17/1570046165172224/1570046170284032/STEM/a1ef884a943d4f3fb0280def90a6421e.png?resizew=151)
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