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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12卷引用:2014届甘肃省兰州一中高考模拟一理科数学试卷
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9-10高二下·海南·期末
真题
名校
2 . 如图,已知AP是⊙O的切线,P为切点,AC是⊙O的割线,与⊙O交于B、C两点,圆心O在
的内部,点M是BC的中点.
![](https://img.xkw.com/dksih/QBM/2010/8/13/1569813231534080/1569813236572160/STEM/b6f90bfca2dc491d8eb11c5269ac68ae.png?resizew=168)
(1)证明A,P,O,M四点共圆;
(2)求∠OAM+∠APM的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32986401a4d24904d5e446fa9210ac6.png)
![](https://img.xkw.com/dksih/QBM/2010/8/13/1569813231534080/1569813236572160/STEM/b6f90bfca2dc491d8eb11c5269ac68ae.png?resizew=168)
(1)证明A,P,O,M四点共圆;
(2)求∠OAM+∠APM的大小.
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14卷引用:2017届甘肃会宁县一中高三上学期9月月考数学(理)试卷
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名校
3 . 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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名校
4 . 如下图
中,
是边
上一点,若
,且
,则
=_________ .
![](https://img.xkw.com/dksih/QBM/2017/9/2/1765587576037376/1766957879009280/STEM/931520655f8a417795c3ee6e0df728b6.png?resizew=240)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/318316db47ee5ac724098ed4e9c9e20b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0762046501add3c10dc910a18bef799d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3fa50c3f82f8a02c0bf4f2d16fe0791.png)
![](https://img.xkw.com/dksih/QBM/2017/9/2/1765587576037376/1766957879009280/STEM/931520655f8a417795c3ee6e0df728b6.png?resizew=240)
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5 . 如图,已知
是圆
的直径,点
是圆
上一点,过点
作圆
的切线,交
的延长线与点
,过点
作
的垂线,交
的延长线与点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/33731ab8-eae0-4a04-8dde-11a92c42bb13.png?resizew=200)
(1)求证:
为等腰三角形;
(2)若
,
,求圆
的面积.
![](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/8455657dde27aabe6adb7b188e031c11.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/33731ab8-eae0-4a04-8dde-11a92c42bb13.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f8ef1ba8effc127569454ecb50e3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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6 . 选修4-1:几何证明选讲
如图,
为
的直径,
切
于点
,
交
于点
,
,点
在
上,求证:
是
的切线.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490b9624a31f9c93fa27b978da7b1719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://img.xkw.com/dksih/QBM/2016/11/9/1573137234911232/1573137241047040/STEM/1a11e46902294b4492db9ac941b5b600.png)
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10-11高三上·河南·阶段练习
7 . 如图,
是圆
的直径,
,
为圆
上的点,
是
的角平分线,过点
作
交
的延长线于
点,
,垂足为点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/10/ea991b84-aac6-49ed-aeb1-ebb99c5317c2.png?resizew=219)
(1)求证:
是圆
的切线;
(2)求证:
.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac37366d2b54dc7d9a95ac6ddda5f3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5fd65265f85df7d149d83d80d4e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b47a08a25693bbfa01026573625ad15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/10/ea991b84-aac6-49ed-aeb1-ebb99c5317c2.png?resizew=219)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f1a6063aa2e76edcfe68c9a268b979.png)
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2016-12-04更新
|
363次组卷
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7卷引用:2017届甘肃省肃南裕固族自治县第一中学高三上学期期末考试数学(理)试卷1
2017届甘肃省肃南裕固族自治县第一中学高三上学期期末考试数学(理)试卷12017届甘肃省肃南裕固族自治县第一中学高三上学期期末考试数学(理)试卷2(已下线)2011届河南省豫南九校高三上学期第二次联考理科数学卷(已下线)2011届河南省郑州市高三第一次质量预测数学文卷2016届青海省平安一中高三4月月考理科数学试卷2016届青海省平安一中高三4月月考文科数学试卷湖北省黄冈市外国语学校2022-2023学年高一下学期(鄂东南省级示范高中教育教学改革联盟学校)期中联考模拟数学试题
8 . 选修4-1:几何证明选讲
如图所示,锐角三角形
的内心为
,过点
作直线
的垂线,垂足为
,点
为圆
与边
的切点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/d3136f72-1d75-4c3b-814a-313b8f3664dd.png?resizew=210)
(1)求证
四点共圆;
(2)若
,求
的度数.
如图所示,锐角三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9020059d62af7498039f091de6f005ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/d3136f72-1d75-4c3b-814a-313b8f3664dd.png?resizew=210)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5ffeb7afe89532dd57766ce0bb711b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c157441734cc2f1853bb3e15b631a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4365bff308dbfd283e4f12ede24de1b3.png)
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2016-12-04更新
|
159次组卷
|
3卷引用:2016届甘肃省天水市一中高三上学期期末理科数学试卷
9 . 如图,四边形
内接于⊙
,过点
作⊙
的切线
交
的延长线于
,已知
.
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092621201408/1572092626673664/STEM/aed405f782ef47e5b84d71a53adb26a7.png?resizew=208)
证明:(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cb8be4bf861579213f88f6d09b13d9.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092621201408/1572092626673664/STEM/aed405f782ef47e5b84d71a53adb26a7.png?resizew=208)
证明:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ddd49625097d0a78df7170be4f882e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3efe45bee98a0436b6e1ae34b377bb1b.png)
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2016-12-03更新
|
508次组卷
|
8卷引用:2016届甘肃省兰州一中高三12月月考理科数学试卷
2012·河北石家庄·一模
名校
10 . 选修4-1:几何证明选讲
已知
中,
,D为
外接圆劣弧AC上的点(不与点A、C重合),延长BD至E,延长AD交BC的延长线于F.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/19/1f54aced-1257-4dbf-b956-8ee412ca35a3.png?resizew=179)
(1)求证:
;
(2)求证:
.
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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12卷引用:2017届甘肃高台县一中高三理上学期检测五数学试卷
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