1 . 如图,AB为⊙O的直径,BD是⊙O的切线,连接AD交⊙O于E,若BD∥CE,AB交CE于M,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b0311cb57d78f465a57dc7f26353c.png)
![](https://img.xkw.com/dksih/QBM/2018/12/5/2090404214185984/2094345211813888/STEM/647c1bdc-8188-4995-bad2-424c20db0e6d.png)
您最近一年使用:0次
名校
2 . 选修4-1:几何证明选讲
已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110d9c6d1908a3a8d188f2b91c1d0070.png)
外接圆劣弧
上的点(不与点
、
重合),延长
至
, 延长
交
的延长线于
.
![](https://img.xkw.com/dksih/QBM/2018/1/17/1862245053358080/1868569482780672/STEM/2d56fb4217b447bbafff448cca50a81e.png?resizew=156)
(Ⅰ)求证:
;
(Ⅱ)求证:
.
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110d9c6d1908a3a8d188f2b91c1d0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e2c719caf927d253ad88a829948039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2018/1/17/1862245053358080/1868569482780672/STEM/2d56fb4217b447bbafff448cca50a81e.png?resizew=156)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4748010af2b117057264c79b90fb203a.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06561de2ef3074de18a272915a6d303d.png)
您最近一年使用:0次
2011·宁夏银川·二模
3 . 在
中,
,过点
的直线与其外接圆交于点
,交
延长线于点
.
![](https://img.xkw.com/dksih/QBM/2011/4/20/1570124972236800/1570124977684480/STEM/a6929cd0a7f340d086fbfabc5495dc7d.png?resizew=216)
(1)求证:
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2011/4/20/1570124972236800/1570124977684480/STEM/a6929cd0a7f340d086fbfabc5495dc7d.png?resizew=216)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899408580730ada2e8d9f8809bb1496f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17ce2318447b226bfe6c8f0fb60a8ed.png)
您最近一年使用:0次
2012·海南省直辖县级单位·一模
4 . 如图设
为线段
中点,
与
交于点
,且
交
于
交
于
.
![](https://img.xkw.com/dksih/QBM/2012/3/20/1570811241472000/1570811247280128/STEM/3bb7730a3928426e89459eab1ee1f473.png?resizew=194)
(1)写出图中三对相似三角形,并对其中一对作出证明;
(2)连结
,设
,求
长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be36353f9b1353cb9a38bc26e814521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fc65594f2151899374acf2c7cf1a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/2012/3/20/1570811241472000/1570811247280128/STEM/3bb7730a3928426e89459eab1ee1f473.png?resizew=194)
(1)写出图中三对相似三角形,并对其中一对作出证明;
(2)连结
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31eee31191f484a7c5b391cde9f19ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
您最近一年使用:0次
10-11高二下·辽宁抚顺·期末
5 . 如图,△ABC内接于⊙O,过点A的直线交⊙O于点P,交BC的延长线于点D,且
AB2=AP•AD.
(1)求证:AB=AC;
(2)如果∠ABC=60°,⊙O的半径为1,且P为
的中点,求AD的长.
AB2=AP•AD.
(1)求证:AB=AC;
(2)如果∠ABC=60°,⊙O的半径为1,且P为
![](https://img.xkw.com/dksih/QBM/2011/7/14/1570257915494400/1570257920811008/STEM/45d76139383a47e49c29b4c031b66e6c.png?resizew=18)
![](https://img.xkw.com/dksih/QBM/2011/7/14/1570257915494400/1570257920811008/STEM/f712f2fd5143465aae89e8550e2ad88b.png?resizew=198)
您最近一年使用:0次
6 . 选修4—1:几何证明选讲
如图,
内接于圆
,
平分
交圆
于点
,过点
作圆
的切线交直线
于点
.
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572073022324736/1572073028354048/STEM/8b152a1213744b2fa0813ae3d7523138.png)
(1)求证:
;
(2)求证:
.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2333da32638ec636fa1e69e750ca4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6062582a0a1679aa777451f25008411d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572073022324736/1572073028354048/STEM/8b152a1213744b2fa0813ae3d7523138.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96db6ed42a67239083c6b36475147e3c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5777d129b34192134305e1c61e60876.png)
您最近一年使用:0次
2011·河南洛阳·一模
7 . 在△ABC中,AB=AC,过点A的直线与其外接圆交于点P,交BC延长线于点D.
(1)求证:
;
(2)若AC=3,求AP•AD的值.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f44caa95b907ab06f85da6f52b9213.png)
(2)若AC=3,求AP•AD的值.
![](https://img.xkw.com/dksih/QBM/2011/2/28/1570019776937984/1570019782385664/STEM/9c20ec07a9c642d29d236e8536c83727.png?resizew=252)
您最近一年使用:0次
2011·河南·一模
8 . 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)
您最近一年使用:0次
2011·山西·一模
9 . 选做题(10分.请考生必须在22、23题中任选一题做答,如果多做,则按所做的第一题记分)
22.
选修4-1:几何证明选讲
在△ABC中,AB=AC,过点A的直线与其外接圆交于点P,交BC延长线于点D.
(Ⅰ)求证:
;
(Ⅱ)若AC=2,求AP•AD的值.
22.
选修4-1:几何证明选讲
在△ABC中,AB=AC,过点A的直线与其外接圆交于点P,交BC延长线于点D.
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f44caa95b907ab06f85da6f52b9213.png)
(Ⅱ)若AC=2,求AP•AD的值.
![](https://img.xkw.com/dksih/QBM/2011/3/9/1570032299630592/1570032305381376/STEM/fd92e888cb9043e0bcd8d3422ae0a244.png?resizew=216)
您最近一年使用:0次