真题
1 . 选修4-1:几何证明选讲
如图AB是
直径,AC是
切线,BC交
与点E.
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/4728723fed18470d84dbc7e44107ef4f.png)
(Ⅰ)若D为AC中点,求证:DE是
切线;
(Ⅱ)若
,求
的大小.
如图AB是
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/f611407c50d540ad9104c02c63aee4ba.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/f611407c50d540ad9104c02c63aee4ba.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/f611407c50d540ad9104c02c63aee4ba.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/4728723fed18470d84dbc7e44107ef4f.png)
(Ⅰ)若D为AC中点,求证:DE是
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/f611407c50d540ad9104c02c63aee4ba.png)
(Ⅱ)若
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/67dc69fe27884a1a8ff1aaa71bdd61c7.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572143053012992/1572143059132416/STEM/ce093531127143b1baddcccf84486568.png)
您最近一年使用:0次
真题
2 . 如图所示,过
外一点
作一条直线与
交于
,
两点,已知
,点
到
的切线长
,则弦
的长为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fca8c94add435f4aefb933ffe55a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
3 . 如图,直线PQ与⊙O相切于点A,AB是⊙O的弦,∠PAB的平分线AC交⊙O于点C,连结CB,并延长与直线PQ相交于点Q,若AQ=6,AC=5.
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572607145648128/1572607151489024/STEM/0359539e1f0c4416859950790998664e.png)
(Ⅰ)求证:QC2﹣QA2=BC
QC;
(Ⅱ)求弦AB的长.
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572607145648128/1572607151489024/STEM/0359539e1f0c4416859950790998664e.png)
(Ⅰ)求证:QC2﹣QA2=BC
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b18d78c40ce368f60208949c5ae3fb.png)
(Ⅱ)求弦AB的长.
您最近一年使用:0次
2016-12-04更新
|
507次组卷
|
3卷引用:2016届河北省衡水中学高三下学期二调考试理科数学试卷
名校
4 . 如图所示,已知直线
的方程为
,⊙
,⊙
是相外切的等圆.且分别与坐标轴及线段
相切,
,则两圆半径![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
__________ (用常数
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f6e613ffa032e7e893daa1970d3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2bc7331e651f466890b46111b962e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/4c1689d5-6d77-40e0-b08d-9da2426bc4fc.png?resizew=171)
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2018-05-25更新
|
184次组卷
|
2卷引用:【全国百强校】安徽省合肥市第一中学2018冲刺高考最后1卷理科数学试卷
5 . 如图,四边形
是圆的内接四边形,
,
、
的延长线交于点
.求证:
平分
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb67f27bcda7681b19239a199b4c4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c36ff76f9f1ee12db562cde7a58b8c3.png)
![](https://img.xkw.com/dksih/QBM/2018/10/15/2054409853542400/2059748077608960/STEM/ba59d31e-853f-4f57-bf17-fd8d5365e04d.png?resizew=328)
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6 . 如图,已知
是
的外接圆,AB=BC,AD是BC边上的高,AE是
的直径.
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989963776/STEM/50c3e0070b13459e883842f9cf513f57.png)
(1)求证:
;
(2)过点C作
的切线交BA的延长线于点F,若AF=4,CF=6,求AC的长.
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989963776/STEM/8ab2ae51d7c84c7f98fd027a2c02eb9b.png)
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989963776/STEM/7fb14140b7684ef190294171f8650ae5.png)
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989963776/STEM/8ab2ae51d7c84c7f98fd027a2c02eb9b.png)
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989963776/STEM/50c3e0070b13459e883842f9cf513f57.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989963776/STEM/0bba7a92d47346738d69885b23e69e35.png)
(2)过点C作
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989963776/STEM/8ab2ae51d7c84c7f98fd027a2c02eb9b.png)
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7 . 选修4-1:几何证明选讲
如图,在
中,
,以
为直径的圆
交
于点
,点
是
边的中点,连接
交圆
于点
.
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/5d33ff30059d4cac9918bc5566fc1a03.png)
(Ⅰ)求证:
是圆
的切线;
(Ⅱ)求证:
.
如图,在
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/b795d5170ea74e0e8ae5ac32c6998610.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/e166a52448f24d6aaf34c5b1f1d2bd89.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/cc4d42c8f44c4d89a5f831db226ff5fe.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/a06e96af970c4255ab0e1a25a0182cc4.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/f7c4c4ac5cb74dbea267c0635e8ee041.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/b8bea577d29844e395c7fe20cefe6d96.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/4f683afe39f94899bbe589b1116ed51d.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/d6f266ed4ce54a349855dcf395fa530b.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/1a8affa475dd441ab6bbcd06cd8aad47.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/a06e96af970c4255ab0e1a25a0182cc4.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/40cb78bd42834166ae60afb21a8c15be.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/5d33ff30059d4cac9918bc5566fc1a03.png)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/ab7882026c6445f0bf667ad98269ccfc.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/a06e96af970c4255ab0e1a25a0182cc4.png)
(Ⅱ)求证:
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572035386146816/1572035392274432/STEM/22bf2fb0368c4a5cb99a0d7c5356fb8a.png)
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8 . 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
9 . 如图所示,在⊙O中,相交于点E的两弦AB,CD的中点分别是M,N,直线MO与直线CD相交于点F.证明
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/cdcc2cdf-e541-42c8-bbce-48c05d3a473d.png?resizew=240)
(1)∠MEN+∠NOM=180°;
(2)FE·FN=FM·FO.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/cdcc2cdf-e541-42c8-bbce-48c05d3a473d.png?resizew=240)
(1)∠MEN+∠NOM=180°;
(2)FE·FN=FM·FO.
您最近一年使用:0次
10 . 如图,在△ABC中,∠C=90°,AC=8 cm,AB=10 cm,点P由C出发以每秒2 cm的速度沿线段CA向点A运动(不运动至A点),⊙O的圆心在BP上,且⊙O分别与AB、AC相切,当点P运动2 s时,⊙O的半径是( )
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844424704/STEM/6f215c156a5e4376b8b1fb61b4dcfa95.png?resizew=139)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844424704/STEM/6f215c156a5e4376b8b1fb61b4dcfa95.png?resizew=139)
A.![]() | B.![]() | C.![]() | D.2 cm |
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