1 . 如图,
是半圆
的直径,
在
的延长线上,
与半圆
相切于点
,
.若
,
,则圆
的半径为,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8e49d68afab33806a63d25a0861c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eea78bf026d76f1cb9cc3dc9349a193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8825d400f453c5c17a7beeb1cc9a9cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
![](https://img.xkw.com/dksih/QBM/2015/5/11/1572096979369984/1572096984530944/STEM/44dc9715f8e544299d03d2c6509ee922.png?resizew=171)
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2 . 与直线
和圆
都相切的半径最小的圆的方程是___________
![](https://img.xkw.com/dksih/QBM/2011/8/17/1570286949228544/1570286954348544/STEM/2e770812f7124ae2aeb971dc2e38e386.png?resizew=77)
![](https://img.xkw.com/dksih/QBM/2011/8/17/1570286949228544/1570286954348544/STEM/064c213e4a514698b2a98dae7ed2752b.png?resizew=128)
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3 . 选修4-1:几何证明选讲
已知线段
为圆
的直径,
为圆周上一点,
于
,过
作圆
的切线交
的延长线于
,过
作
垂直
的延长线于
,求证:
![](https://img.xkw.com/dksih/QBM/2016/7/1/1572855368957952/1572855375372288/STEM/dc52e086a95a41c59d55972d94ede4db.png)
(1)
;
(2)
.
已知线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17be90850a55d8b037e15d45de2bab0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2016/7/1/1572855368957952/1572855375372288/STEM/dc52e086a95a41c59d55972d94ede4db.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1b2dbd754b0f8de472b260c576f064.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d212c1709b8e72a055cf1b5381ef64.png)
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4 . 如图
是
的内接三角形,
是
的切线,切点为
,
,
交
于点
,交
于点
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/2a357bcc87c648ff8fedfef040b2d524.png)
(1)求
的面积;
(2)求弦
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef227e3c17e425d6809b50489f83f50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/a505918f471e4a75acd1e75c2fa893be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/55f102b88f6e4d7194986939500fa96b.png)
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/47b4566bbb7a4c1099b73275908b7096.png)
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/7674e6f9d5044cf69c2fce1d5ff82eea.png)
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/0864a8e4010a4770a8d4737ba2ccdeaa.png)
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/2a357bcc87c648ff8fedfef040b2d524.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2016/6/23/1572806612631552/1572806618841088/STEM/93ce5f8adad84adbb71949c09fc08280.png)
(2)求弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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5 . 选修4-1:几何证明选讲.
如图
是圆
的一条弦,过点
作圆的切线
,作
,与该圆交于点
,若
,
.
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573025500635136/1573025506861056/STEM/36ef016aad6e4e0c867c34a9f4a60800.png)
(1)求圆
的半径;
(2)若点
为
中点,求证
三点共线.
如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759f49569f2079bc4df67f06a32eb8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573025500635136/1573025506861056/STEM/36ef016aad6e4e0c867c34a9f4a60800.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b07ea040f925308c31116cf77c113a.png)
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2011·广东广州·一模
6 . 在梯形ABCD中,AD∥BC,AD=2,BC=5,点E、F分别在AB、CD上,且EF∥AD,若
,则EF的长为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44713ca253b0ed70a51819b05692676e.png)
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2011·新疆·一模
7 . 如图,已知⊙
的直径
,
为圆周上一
点,
,过点
作⊙
的切线
,过点
作
的垂线
,垂足为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0b71b8d2c183154221f717ce09077b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
![](https://img.xkw.com/dksih/QBM/2011/3/29/1570085169635328/1570085174706176/STEM/8f38bbfcf7a143eabf6a04e6a4cf2615.png?resizew=177)
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8 . 选修4-1:几何证明选讲
如图,在圆内接梯形
中,
,过点
作圆的切线与
的延长线交于点
,若
.
![](https://img.xkw.com/dksih/QBM/2016/11/9/1573135186075648/1573135192621056/STEM/372423e4bab74565b97a7e6485573625.png)
(1)求证:梯形
为等腰梯形;
(2)求弦
的长.
如图,在圆内接梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e2dbfad0bc120f503e4d23b384280.png)
![](https://img.xkw.com/dksih/QBM/2016/11/9/1573135186075648/1573135192621056/STEM/372423e4bab74565b97a7e6485573625.png)
(1)求证:梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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2011·河南·一模
9 . 如图,已知AD是△ABC的外角∠EAC的平分线,交BC的延长线于点D,延长DA交△ABC的外接圆于点F,连接FB,FC.
(1)求证:FB=FC;
(2)求证:FB2=FA•FD;
(3)若AB是△ABC外接圆的直径,且∠EAC=120°,BC=6,求AD的长.
(1)求证:FB=FC;
(2)求证:FB2=FA•FD;
(3)若AB是△ABC外接圆的直径,且∠EAC=120°,BC=6,求AD的长.
![](https://img.xkw.com/dksih/QBM/2011/4/16/1570120503336960/1570120508833792/STEM/006578c216cd435bbee6e3d487477cea.png?resizew=213)
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10 . 选修4-1:几何证明选讲
如图,已知
是
的外角
的平分线,交
的延长线于点
,延长
交
的外接
圆于点
,连结
.
![](https://img.xkw.com/dksih/QBM/2016/8/24/1572992052699136/1572992059105280/STEM/faa8b2cb2dfb439d87c61ccb345abf2d.png)
(1)求证:
;
(2)若
,求
的长.
如图,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6344778ed1e75c1a99e2268468081867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
圆于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa175408eddbdfddfbe9701646d62b92.png)
![](https://img.xkw.com/dksih/QBM/2016/8/24/1572992052699136/1572992059105280/STEM/faa8b2cb2dfb439d87c61ccb345abf2d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07b92b8282c7fd1158b3b5098e38c39.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddfcdeed612c9976ecaca2d2b63d14d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
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