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)
您最近一年使用:0次
2019-01-30更新
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3930次组卷
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12卷引用:2016届湖北省宜昌市一中高三上学期12月月考数学试卷
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 . 选修4-1:几何证明选讲
已知
中,
,
是
外接圆劣弧
上的点(不与点
重合),延长
至
,延长
至
.
![](https://img.xkw.com/dksih/QBM/2016/9/7/1573002676461568/1573002682957824/STEM/30ee776e7b61401489a3ac69ce006b2d.png)
(1)求证:
;
(2)若
,
中
边上的高为
,求
外接圆的面积.
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2016/9/7/1573002676461568/1573002682957824/STEM/30ee776e7b61401489a3ac69ce006b2d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b9fad2d1591b8141849ddece51b83a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea2ab040c9654f0b3ed5150c9b55bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
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3 . 选修4-1:几何证明选讲
已知
中,
,
是
外接圆劣弧
上的点(不与点
重合),延长
至
,延长
至
.
![](https://img.xkw.com/dksih/QBM/2016/8/29/1572993393975296/1572993400332288/STEM/1afd1d951ceb4b30898ba321ce6eb3fd.png)
(1)求证:
;
(2)若
,
中
边上的高为
,求
外接圆的面积.
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2016/8/29/1572993393975296/1572993400332288/STEM/1afd1d951ceb4b30898ba321ce6eb3fd.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/8/29/1572993393975296/1572993400332288/STEM/6884cfed20cd46b8ab078e06d511891f.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2016/8/29/1572993393975296/1572993400332288/STEM/1d9b35d6bd424107abd3d87504c95643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://img.xkw.com/dksih/QBM/2016/8/29/1572993393975296/1572993400332288/STEM/ee879a4715cf4e3abb17215041d4f3fb.png)
![](https://img.xkw.com/dksih/QBM/2016/8/29/1572993393975296/1572993400332288/STEM/27500c9f971241e7ad4eb293882bc7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
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4 . 如图,正方形
边长为
,以
为圆心,
为半径的圆弧与以
为直径的半圆
交于点
,连结
并延长交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/070efbd967784b7bb09a6176db944c29.png)
(1)求证:
为
的中点;
(2)求
的值.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/57453c6f2806415dab410ba1b4f05cef.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/4455298339f64896b359b953d34294b8.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/6f45f2742cd04744a8e8bb95ad17f554.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/82f15f28b652475c8344ca151698aead.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/066228d43a0840e1a4d89cff04c0be44.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/477875ee3fcf4557b30a82e77722757e.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/4a77b55c5c784fd4aab7506b11c35474.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/7b95841e2cdb41ee80ed7e631a4fa4e9.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/ac61771f1a8b4e66b90926c0dc33c8a3.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/92437732da6c448da5bf61877e777755.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/070efbd967784b7bb09a6176db944c29.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/92437732da6c448da5bf61877e777755.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/ac61771f1a8b4e66b90926c0dc33c8a3.png)
(2)求
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/9c2381ceba2e4d8fa62a17436d7892d3.png)
您最近一年使用:0次
5 . (选修4—1:几何证明选讲)
如图,已知切线
切圆于点
,割线
分别交圆于点
,点
在线段
上,且
,
,
,
,则线段
的长为________ .
如图,已知切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.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/c59802bde1dc59ba9000157b08463b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42f5b34fe7c05319216eca3541ec4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3077b532022113b4d85d47d730de23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b336e518ac4ff04c6c26e4b8a15844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572244196278272/1572244202061824/STEM/21a2924585af4c67b8b1e3cd0b05b3a5.png?resizew=144)
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6 . 如图,延长△ABC的角平分线AD交其外接圆于E,若AD =AB= 1,DE =
,则AC=_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572126201487360/1572126207524864/STEM/460448641459437db3c1fec97ab5ba10.png?resizew=144)
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7 . (选修4-1:几何证明选讲)如图,PB为△ABC外接圆O的切线,BD平分
,交圆O于D,C,D,P共线.若
,
,
,则圆
的半径是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404fc19da3e4da41e9147e9f0ca64957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8915e8e775538d41debf1933102c6b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99f724bb3614b40d63b284abaa7993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122493845504/1572122499538944/STEM/6681d77159a146babcb660a06bb6b8c0.png?resizew=138)
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8 . (选修4-1:几何证明选讲)如图,
是⊙
的直径,
是⊙
上的两点,
⊥
,过点
作⊙
的切线FD交
的延长线于点
.连结
交
于点
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
_____ .
![](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/ea9aa3f533894ca87a394f7a1dfd0ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/8455657dde27aabe6adb7b188e031c11.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://staticzujuan.xkw.com/quesimg/Upload/formula/d131688ea412debccba8b3860ccf60dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
![](https://img.xkw.com/dksih/QBM/2015/6/10/1572120852537344/1572120858542080/STEM/75c9f6f4d4294f87a380c7ee6f50c622.png?resizew=265)
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