10-11高二下·辽宁抚顺·期末
1 . 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)
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10-11高二下·河南郑州·阶段练习
2 . .选修4-1:几何证明选讲
已知
ABC中,AB=AC, D是
ABC外接圆劣弧AC弧上的点(不与点A,C重合),延长BD至E.
(1)求证:AD的延长线平分
CDE;
(2)若
BAC=30°,
ABC中BC边上的高为2+
,
求
ABC外接圆的面积.
已知
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
(1)求证:AD的延长线平分
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/fb0457dd18ff453aa76a046a9e445e0a.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/fb0457dd18ff453aa76a046a9e445e0a.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/4e5551f105934d3a9c4ebe6be17ac12d.png)
求
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/37f0b721192d4235a13bfbfd0f01f5d5.png)
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11-12高三上·河南洛阳·期末
3 . 选修4-1:几何证明选讲
如图,在△ABC中,∠ABC=90°,以BC为直径的圆O交
![](https://img.xkw.com/dksih/QBM/2011/5/19/1570209865703424/1570209870929920/STEM/0ae9fb78725341509c77d9d9f138fd59.png?resizew=89)
AC于点D,设E为AB的中点.
(1)求证:直线DE为圆O的切线;
(2)设CE交圆O于点F,求证:CD·CA=CF·CE.
如图,在△ABC中,∠ABC=90°,以BC为直径的圆O交
![](https://img.xkw.com/dksih/QBM/2011/5/19/1570209865703424/1570209870929920/STEM/0ae9fb78725341509c77d9d9f138fd59.png?resizew=89)
AC于点D,设E为AB的中点.
(1)求证:直线DE为圆O的切线;
(2)设CE交圆O于点F,求证:CD·CA=CF·CE.
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4 . 已知圆
的方程为:
,直线的方程为
,点
在直线上,过点
作圆
的切线
,切点为
.
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/33bca3e29e0c4b7f9d5131abd5ea9285.png)
(1)若
,求点
的坐标;
(2)若点
的坐标为
,过点
的直线与圆
交于
两点,当
时,求直线
的方程;
(3)求证:经过
(其中点
为圆
的圆心)三点的圆必经过定点,并求出所有定点的坐标.
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/3d5032b8e16a48278074a9b13b8ea604.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/6abf4320c25a4066a7e2a24e538245ee.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/9d100565713a4563a2fd17c899a1607e.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/4c31d272157744d7be133a5531fb8d1f.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/4c31d272157744d7be133a5531fb8d1f.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/3d5032b8e16a48278074a9b13b8ea604.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/baabd968640d4c81a564d36fdafe7bb7.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/52b6d604ae434a779657ffd90d2bde4f.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/33bca3e29e0c4b7f9d5131abd5ea9285.png)
(1)若
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/a04519a6852340caa2812a0efeb7725e.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/4c31d272157744d7be133a5531fb8d1f.png)
(2)若点
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/4c31d272157744d7be133a5531fb8d1f.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/0845fad52439481babaf3375ad63f674.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/4c31d272157744d7be133a5531fb8d1f.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/3d5032b8e16a48278074a9b13b8ea604.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/984da381678a48959f776f3216d78b9f.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/69d161424141467b8315d21609279a9e.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/279b4101d173432fbb45f681faed7d73.png)
(3)求证:经过
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/be2e2157747d4fe5b7d90b4757732f45.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/3d5032b8e16a48278074a9b13b8ea604.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585937055744/STEM/3d5032b8e16a48278074a9b13b8ea604.png)
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10-11高二下·海南·期末
5 . 如图,PAB,PCD是
的割线,PQ是
的切线,连接AC,AD,若∠PAC=∠BAD.
![](https://img.xkw.com/dksih/QBM/2011/4/18/1570122042114048/1570122047488000/STEM/fd8b06feca6f424c833de1f636f42379.png?resizew=218)
求证:
(1)PA·PB=AC·AD;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://img.xkw.com/dksih/QBM/2011/4/18/1570122042114048/1570122047488000/STEM/fd8b06feca6f424c833de1f636f42379.png?resizew=218)
求证:
(1)PA·PB=AC·AD;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efaed3417c545c5f51db5b81e4af985c.png)
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10-11高二下·海南·期末
6 . 如图:
为
的外接圆,
,过点
的直线交
于
,交
延长线于
,
是
的延长线,连接
.
![](https://img.xkw.com/dksih/QBM/2011/4/18/1570122042114048/1570122047381504/STEM/4477dad8d0c549489597dd2fee3dbd7f.png?resizew=180)
① 求证:
;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2011/4/18/1570122042114048/1570122047381504/STEM/4477dad8d0c549489597dd2fee3dbd7f.png?resizew=180)
① 求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14072216fabe3e325e8f0da087239b1e.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607b3dca43bf4454f1ec2661f722f8f2.png)
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11-12高三上·广东·期末
7 . 如图,圆
的直径
为圆周上一点,
,过
作圆的切线
,过
作直线
的垂线
为垂足,
与圆
交于点
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801e4d9f1e724f7e310657bdf046220.png)
![](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/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/c6cf11f0cc16be9c0301d0dc554cd7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/2011/3/1/1570020512923648/1570020517781504/STEM/0d2cbcbe241649329280f711884e2917.png?resizew=139)
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2010高三·全国·专题练习
真题
8 . 如图,△ABC的角平分线AD的延长线交它的外接圆于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e28ce60503fab70ce1797449d90dadc.png)
(Ⅰ)证明:△ABE∽△ADC;
(Ⅱ)若△ABC的面积
,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e28ce60503fab70ce1797449d90dadc.png)
(Ⅰ)证明:△ABE∽△ADC;
(Ⅱ)若△ABC的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec4fccf16c3064c1fe33098ec3e8ae2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://img.xkw.com/dksih/QBM/2011/2/25/1570012428500992/1570012433973248/STEM/a38682262ddd43fea44e49fb2f7163c1.png?resizew=152)
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2016-11-30更新
|
403次组卷
|
9卷引用:2010年高考试题分项版文科数学之专题十七 选修系列
(已下线)2010年高考试题分项版文科数学之专题十七 选修系列2010年普通高等学校招生全国统一考试(辽宁卷)文科数学全解全析(已下线)2011届宁夏贺兰一中高三上学期期末考试数学理卷(已下线)2011-2012学年河南省周口市高二下学期四校第一次联考文科数学试卷(已下线)2013-2014学年河北省石家庄市高二下学期期末考试理科数学试卷2015届甘肃省河西三校普通高中高三上学期第一次联考理科数学试卷2015届甘肃省河西三校普通高中高三上学期第一次联考文科数学试卷2017届广东珠海市高三9月摸底考试数学(理)试卷河南省郑州市巩义中学2019-2020学年高二下学期期中考试数学(文)试题
11-12高三上·江苏泰州·期末
9 . 如图,
是边长为
的正方形,以
为圆心,
为半径的圆弧与以
为直径的半⊙O交于点
,延长
交
于
.
![](https://img.xkw.com/dksih/QBM/2011/1/12/1569964573884416/1569964579012608/STEM/cd35b21af7eb419481fcc026109f671e.png?resizew=136)
(1)求证:
是
的中点;
(2)求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2011/1/12/1569964573884416/1569964579012608/STEM/cd35b21af7eb419481fcc026109f671e.png?resizew=136)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
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