真题
1 . 选修4—1:几何证明选讲 如图,直线AB为圆的切线,切点为B,点C在圆上,∠ABC的角平分线BE交圆于点E,DB垂直BE交圆于D.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/5365865e-1cc9-47a2-9e47-f3464ca9a3c5.png?resizew=160)
(Ⅰ)证明:DB=DC;
(Ⅱ)设圆的半径为1,BC=
,延长CE交AB于点F,求△BCF外接圆的半径.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/5365865e-1cc9-47a2-9e47-f3464ca9a3c5.png?resizew=160)
(Ⅰ)证明:DB=DC;
(Ⅱ)设圆的半径为1,BC=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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2019-01-30更新
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3925次组卷
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12卷引用:2014年高考数学文二轮专题复习与测试选修4-1几何证明选讲练习卷
(已下线)2014年高考数学文二轮专题复习与测试选修4-1几何证明选讲练习卷2013年全国普通高等学校招生统一考试理科数学(新课标1卷)2013年全国普通高等学校招生统一考试文科数学(新课标1卷)(已下线)2014届甘肃省兰州一中高考模拟一理科数学试卷(已下线)2014届甘肃省兰州一中高考模拟一文科数学试卷2015届黑龙江省哈尔滨六中高三上学期期末考试理科数学试卷2015届江西省吉安市第一中学高三上学期第二次阶段考试文科数学试卷2015届陕西省西安长安区一中高三上学期第三次质检理科数学卷2015届陕西省西安长安区一中高三上学期第三次质检文科数学卷2016届甘肃省会宁县一中高三上第四次月考理科数学试卷2016届湖北省宜昌市一中高三上学期12月月考数学试卷河北省武邑中学2017届高三下学期第一次质检考试数学(文)试题
2 . 在
中,N是边AC上一点,且
,AB与
的外接圆相切,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b50f83fd73b99fc0e0c61d80346e3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa020cb9948ac34d16b37386f05ff36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f3cd6a673d7e238ebb769839b6317a9.png)
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2018-03-07更新
|
148次组卷
|
2卷引用:2018年江苏省高三上学期期末数学试题分类选考之选修4-1:几何证明选讲
3 . 如图,已知
的半径为
,
的半径为
,两圆外切于点
.点
为
上一点,
与
切于点
.若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01ba3f329b712e87ead41125cacd34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
![](https://img.xkw.com/dksih/QBM/2018/2/22/1887858184478720/1892230558900224/STEM/5e0ca53af3d2480a9698b0e16b278341.png?resizew=227)
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2018-02-28更新
|
158次组卷
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2卷引用:2018年江苏省高三上学期期末数学试题分类选考之选修4-1:几何证明选讲
名校
4 . 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)
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5 . 如图,已知
为⊙
的直径,直线
与⊙
相切于点
,
垂直
于点
. 若
,求切点
到直径
的距离
.
![](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/e6e490f703eb6c9bb1278c78ebc2d661.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a19338598965bb3856cdd0236bbf694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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2018-01-18更新
|
172次组卷
|
2卷引用:2018年江苏省高三上学期期末数学试题分类选考之选修4-1:几何证明选讲
2017高三·全国·专题练习
6 . 将形状、大小完全相同的两个等腰三角形如图所示放置,点D在AB边上,△DEF绕点D旋转,腰DF和底边DE分别交△CAB的两腰CA,CB于M,N两点,若CA=5,AB=6,AB=1:3,则MD+
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c537e7fab558d6335afa07c2c5b4b122.png)
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925358351671296/1930322234630144/STEM/1ced2471a7aa4999a84f0e37a88bbb32.png?resizew=155)
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2017高三·全国·专题练习
7 . 如图,在
中,
,点
在
上,
,点
是
上的动点,则
的最小值为
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925358351671296/1930322234548224/STEM/84d7c9c6aea54cf196a1dfe9adba08cb.png?resizew=114)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27ec39ae9fe6c726f04d95d436618f2.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/b0f6fc22fa9a491da7e93d01742a8e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186dee1a1cf68677d143172a2a50709c.png)
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925358351671296/1930322234548224/STEM/84d7c9c6aea54cf196a1dfe9adba08cb.png?resizew=114)
A.4 | B.5 | C.6 | D.7 |
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2017高三·全国·专题练习
8 . 如图,∠AOB的边OB与x轴正半轴重合,点P是OA上的一动点,点N(3,0)是OB上的一定点,点M是ON的中点,∠AOB=30°,要使PM+PN最小,则点P的坐标为______ .
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925358351671296/1930322234466304/STEM/cc53f5ca3aca4af9accaa4c1b553fe1a.png?resizew=220)
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2017高三·全国·专题练习
9 . 如图,MN是⊙O的直径,MN=4,点A在⊙O上,∠AMN=30°,B为
的中点,P是直径MN上一动点.
(1)利用尺规作图,确定当PA+PB最小时P点的位置(不写作法,但要保留作图痕迹).
(2)求PA+PB的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e63f752360194aca10417ca1f467ae.png)
(1)利用尺规作图,确定当PA+PB最小时P点的位置(不写作法,但要保留作图痕迹).
(2)求PA+PB的最小值.
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925358351671296/1930322234613760/STEM/4855f3156a374dd999ab1dad1b2dcb41.png?resizew=143)
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