2010·黑龙江哈尔滨·一模
1 . 选修4-1:几何证明选讲
如图,已知
点在⊙
直径的延长线上,
切⊙
于
点,
是
的平分线,且交
于
点,交
于
点.
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f064c53e1030482cada14b5002913cf0.png)
(1)求
的度数;
(2)若
,求
.
如图,已知
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c9b96029815b4fee956f1dd14b16c519.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c195da6c33724175ad833081f8b6c367.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/658f5ce6c1c24beb9ee7d0862af41c9a.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c195da6c33724175ad833081f8b6c367.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/86e450de1d844ab085556f65f163d0bb.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/3b024db94d38400ab4778285d6a147ed.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/6636f6ff0f0e4d44b6f35a63393fc31d.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/babf31d6a39c44ffb64ca8294ab0d531.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/3f2d4c92974d4a60b3adeefacffd3664.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/4b016ec3d5b544bdbe4990ea634529a5.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/2140925fcb9a4e16937624eb1dfe90f1.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f064c53e1030482cada14b5002913cf0.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/0c51a0a5c8ab4cec8af8be1657b0c9b4.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/58bb7d54d6444190b394bbcc7be1aaeb.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f394ef40aaa64bbf9bba63b22333024d.png)
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2016-12-03更新
|
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6卷引用:黑龙江省哈尔滨市第六中学2010届高三一模数学(理)试题
(已下线)黑龙江省哈尔滨市第六中学2010届高三一模数学(理)试题(已下线)黑龙江省哈尔滨市第六中学2010届高三一模数学(文)试题2015届黑龙江省哈尔滨六中高三下学期第三次模拟理科数学试卷2016届黑龙江省哈尔滨市六中高三上期末理科数学试卷2015届贵州省贵阳市普通高中高三上学期期末监测考试理科数学试卷2015届贵州省贵阳市普通高中高三上学期期末监测考试文科数学试卷
2 . 选修4-1:几何证明选讲.
如图,圆周角
的平分线与圆交于点
,过点
的切线与弦
的延长线交于点
,
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/9a4d7e72-02d8-4427-9ec6-78288d954c03.png?resizew=139)
(1)求证:
;
(2)若
四点共圆,且弧
与弧
相等,求
如图,圆周角
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/9f391813265344e3b84b0add71f8735f.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/53a2deb9e45d47c5a5d523e5f3e9affb.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/53a2deb9e45d47c5a5d523e5f3e9affb.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/42a37ba17bed44ec8b1695afe12d8473.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/e9a7fb85543b434eb8d641b18020d179.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/fdf7e0242d064d49996745aea9a3a32a.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/dafb54ea36c244d6b6cc375a417274fc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/2baab2bea819401da1ece84a3558ff91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/9a4d7e72-02d8-4427-9ec6-78288d954c03.png?resizew=139)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/f134a28849784be185d26d443598825a.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/e08368f8215244b28f869c2170e623e4.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/42a37ba17bed44ec8b1695afe12d8473.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/dafb54ea36c244d6b6cc375a417274fc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/9f391813265344e3b84b0add71f8735f.png)
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2016-12-03更新
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480次组卷
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6卷引用:2015届黑龙江省哈尔滨九中高三第三次高考模拟理科数学试卷
3 . 如图所示,
为以
为直径的圆
的切线,
为切点,
为圆周上一点,
,直线
交
的延长线于点
.
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/a4ce8c32f06244e1a15242a05c5f3c2d.png)
(1)求证:直线
是圆
的切线;
(2)若
,
,求线段
的长.
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/f4d399a4d95f4e4986bc69e8addecbcb.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/d900b01e8d754989b68e7e5da50ae09a.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/4796d7d1550545f5841f0c855f935413.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/1e63e56eea8e48aa93d8b128221a22d6.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/3fe9e2a5e7bd45349202edeae9b53e05.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/c9bded80d9854945bb7cc5c935b41258.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/e2ea61d9b5d34e7a804fb12b7f51d9e7.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/d900b01e8d754989b68e7e5da50ae09a.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/6d6708a57d764cb6ae1494818111cfb8.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/a4ce8c32f06244e1a15242a05c5f3c2d.png)
(1)求证:直线
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/e2ea61d9b5d34e7a804fb12b7f51d9e7.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/4796d7d1550545f5841f0c855f935413.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/6e6758e09a3a4ee9a9f59155b6f7a204.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/390d78d8afa94721bed123c9f813853f.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/04fd07e407c74c8d9b3865d9ef7e322a.png)
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4 . 选修4-1:几何证明选讲
如图,
是圆
的直径,
是半径
的中点,
是
延长线上一点,且
,直线
与圆
相交于点
、
(不与
、
重合),
与圆
相切于点
,连结
,
,
.
![](https://img.xkw.com/dksih/QBM/2015/7/20/1572188398379008/1572188404424704/STEM/6bf2e8a3131c4961abd5f245d2b2aaf1.png)
(Ⅰ)求证:
;
(Ⅱ)若
,求
.
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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef737b051413f81f8e473b7aa2bbfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://img.xkw.com/dksih/QBM/2015/7/20/1572188398379008/1572188404424704/STEM/6bf2e8a3131c4961abd5f245d2b2aaf1.png)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2015/7/20/1572188398379008/1572188404424704/STEM/1dcb487989b7444c8509a3fb64741d88.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c360f6b10ef0051f26059b97c0aa570.png)
![](https://img.xkw.com/dksih/QBM/2015/7/20/1572188398379008/1572188404424704/STEM/e7692430953648a69cb7cc5905e63f2b.png)
您最近一年使用:0次
2016-12-03更新
|
566次组卷
|
2卷引用:2015届黑龙江省哈尔滨市三中高三第四次模拟考试理科数学试卷
2010·黑龙江·二模
5 . 直线
与圆
(
)相交于A,B两点,且弦AB的中点为(0,1),则直线
的方程是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23235e355586f9cbd5c07fdcd46fffb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89e1ee3b8e2751f354aa5ab7135c75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2011·黑龙江·二模
6 . 在△ABC中,已知CM是∠ACB的角平分线,△AMC的外接圆交BC于点N,AC=
AB.求证:BN=2AM
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/2011/4/14/1570118536364032/1570118542041088/STEM/e291bda0644c4a63a04f9b430e10146e.png?resizew=115)
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2011·黑龙江哈尔滨·三模
7 . 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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8 . 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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9 . 选修4-1:几何证明选讲
圆
是以
为直径的圆,延长
与
交于
点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/0af4c3ca-0cdd-4590-b9fa-8c30228df30a.png?resizew=183)
(Ⅰ)求证:
是圆
的切线;
(Ⅱ)
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5762def25feb1ab47465e2d629a8cd.png)
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/0af4c3ca-0cdd-4590-b9fa-8c30228df30a.png?resizew=183)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(Ⅱ)
![](https://img.xkw.com/dksih/QBM/2016/7/12/1572913900216320/1572913906786304/STEM/5587f10125244c48927f92d3b4c46728.png)
![](https://img.xkw.com/dksih/QBM/2016/7/12/1572913900216320/1572913906786304/STEM/56db4f8204bd4e78afc69c77d0c6d2f3.png)
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2016-12-04更新
|
115次组卷
|
2卷引用:2016届黑龙江哈尔滨六中高三下四模考试文科数学试卷
2012·河南焦作·一模
10 . 在
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.
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/13cf603650fe4de19d4d0d65cea4b9fc.png)
(1)求证:
;
(2)若AC=3,求
的值.
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/4068bd6d669d4586b69702cb3762e8c2.png)
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/13cf603650fe4de19d4d0d65cea4b9fc.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/0a245338e40a4c728e67305b45866c4f.png)
(2)若AC=3,求
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/3d841a1467fa49a59809ed6a011bc517.png)
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2016-12-02更新
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9卷引用:2012届黑龙江省哈六中高三第三次模拟考试理科数学试卷
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