1 . 选修4-1:几何证明选讲
如图,AB是⊙O的直径,AD,DE是⊙O的切线,AD,BE的延长线交于点C.
![](https://img.xkw.com/dksih/QBM/2016/10/16/1573072174120960/1573072180314112/STEM/f62b66247fad4e919be28a85272086cc.png)
(1)求证:
四点共圆;
(2)若
,CE=1,
30°,求
长.
如图,AB是⊙O的直径,AD,DE是⊙O的切线,AD,BE的延长线交于点C.
![](https://img.xkw.com/dksih/QBM/2016/10/16/1573072174120960/1573072180314112/STEM/f62b66247fad4e919be28a85272086cc.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be90d18409de7c324059f18a4fd9db7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db966856ec2cbe925bdf8ee29fc93611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d38dd5d46dc279bbe3c20ea4e03fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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2 . 选修4-1:几何证明选讲
如图,
是圆
的直径,
是弦,
的平分线
交圆
于点
,
,交
的延长线于点
,
交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970456940544/1572970463412224/STEM/539a038f94474ab6afa22351b0cffc3e.png)
(1)求证:
是圆
的切线;
(2)若
,圆
的半径为2,
,求
的值.
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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6062582a0a1679aa777451f25008411d.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535a65c61f47d2b893706d4bc3499e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572970456940544/1572970463412224/STEM/539a038f94474ab6afa22351b0cffc3e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae0a715338cd0f509b4001a6e26e85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065f2c3527fcc9d84939c47ac8640643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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3 . 15(几何证明选讲选做题)如图,
是圆
的直径,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd41df221293d5cdbab35be6ae5987e.png)
______
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/6dd94026e36a43a1b1eb042f9fe3dfca.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/03fd77017d714b17b8152e4a47c614e2.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/797c984e40ed4074a9de99b557e9f1cc.png?resizew=68)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/8021a76cfd17480ba5e4d7239a7419a5.png?resizew=103)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd41df221293d5cdbab35be6ae5987e.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/0a2644f1caf54e728fc07e6dbfcc6136.png?resizew=121)
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4 . 如图,四边形ABED内接于⊙O,AB∥DE,AC切⊙O于A,交ED延长线于C. 若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ce519f633407c609e8186a801965e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572032789225472/1572032795017216/STEM/b7da73ac241649459d68e9b177e843ab.png?resizew=135)
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12-13高二下·广东·期末
5 . 如图,A、B是两圆的交点,AC是小圆的直径,D和E分别是CA和CB的延长线与大圆的交点,已知AC=4,BE=10,且BC=AD,求DE的长.
![](https://img.xkw.com/dksih/QBM/2014/2/25/1571529570508800/1571529576112128/STEM/0e017603c63549c8b529b8d41244c9f0.png)
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6 . 如图,已知⊙O的割线PAB交⊙O于A,B两点,割线PCD经过圆心,若PA=3,AB=4,PO=5,则⊙O的半径为______________ .
![](https://img.xkw.com/dksih/QBM/2011/7/26/1570273735401472/1570273740726272/STEM/5abf0315-f664-40fa-b482-652c703f5e02.png)
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10-11高二下·广东汕头·期末
7 . (几何证明选讲选做题)如图所示,圆的内接
的
的平分线
延长后交圆于点
,连接
,已知
,
,
,则线段
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f01c4faacedfe56f5127d6c0cc63cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002767b8780fc8bf7aafc7beb2bae1e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f76e37d6e6b182896ccaaa187cfe07.png)
![](https://img.xkw.com/dksih/QBM/2011/7/20/1570269561085952/1570269565919232/STEM/76244fa834d148938973a97e29d98c1a.png?resizew=85)
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8 . 如上图,EB、EC是⊙O的两条切线,B、C是切点,A、D是⊙O上两点,如果∠E=46°,∠DCF=32°,则∠A的度数是________
![](https://img.xkw.com/dksih/QBM/2011/6/7/1570238435598336/1570238440374272/STEM/5e7c092980854c6290813da476d5c3e1.png?resizew=168)
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11-12高二上·广东·期末
9 . 如图所示,
是圆
的直径,
切圆
于
点,
切圆
于
点,交
的延长线于E点,若
则
=____________ .
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/5f055671ce004955bf3dd47b7d575f6b.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/9c18c943b8a04d10b47b9820fdffb231.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/aec59ba51d4f4f12b86c535b797e2491.png?resizew=25)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/9c18c943b8a04d10b47b9820fdffb231.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/486e129e4f2f48588ae275f345668c25.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/c6b307523ced46c5946b5ef3f04318ef.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/9c18c943b8a04d10b47b9820fdffb231.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/3bbfa158002141859856a7dc80381dd4.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/a20be861511c417e9e677d245ed7ea11.png?resizew=25)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/e62f2bb52e93422eb3acf6d9629865a0.png?resizew=107)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/a07cad2a2e7a4b078060cf523fbe540b.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2011/5/17/1570204967395328/1570204972163072/STEM/5e7de47c-c7ed-4c67-97c6-c87e5a2e56bf.png)
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10 . 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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