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
|
3914次组卷
|
12卷引用: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
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2016届湖北省宜昌市一中高三上学期12月月考数学试卷
2 . 已知:如图所示,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8621d8d46c0ef8ed2548d6773b13a479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56129401e458ce0cc2370296a516340.png)
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472519102464/1619472519561216/STEM/390367b644fb4367903337893430296e.png)
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3 . 如图所示,
为
斜边
边上的中线,
,
,连接
交
于点
,
,
.求证:
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472519102464/1619472519667712/STEM/ee65ac7e5fc04485a9011cf8b6e685c1.png)
(1)
∽
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa8cee7d2463f6f7d352e8b65f47cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6d946ec5bc75341f7e5fe400054464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c3f12229161dd431f7ffdbe7bcfe0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472519102464/1619472519667712/STEM/ee65ac7e5fc04485a9011cf8b6e685c1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f90188bd10aabf5f6faf7dd4bdf2ae.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ce838f38419e8781d63b3417cac5e4.png)
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4 . 如图所示,在
中,
为
的内心,
交
于
,交
外接圆于
.
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472216219648/1619472216768512/STEM/ebcb7c596b434533a33f29987c26af86.png)
求证:(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42774a918f52ac8aa8b1f5b78a676f17.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/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472216219648/1619472216768512/STEM/ebcb7c596b434533a33f29987c26af86.png)
求证:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4aa079ece53f5de96b5367bd343dd53.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c022749480861449780ee16959886a5.png)
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5 . 如图所示,
内接于圆,
切圆于
是
延长线上一点,连接
交
于
点.若
是
的中点.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354e1b631c1f46ed3aa1ce42fe498896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d3f0454a0d7985a9e88d85f13ab9cb.png)
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472216219648/1619472216694784/STEM/5143774fbc6d4441966f6f0a4ca9fbb2.png)
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6 . 如图所示,在等腰三角形
中,
,
为
延长线上一点,
为
延长线上一点,且满足
.
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472519102464/1619472519610368/STEM/fe4c6a8cbbaf490ca3b26ee8b5f79614.png)
(1)求证:
∽
;
(2)若
,求
的读数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/6b1bd1adfe4cc6566218f19970c2fd3b.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/5a840d22a45b6f994cf2dbdddd5e1abc.png)
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472519102464/1619472519610368/STEM/fe4c6a8cbbaf490ca3b26ee8b5f79614.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504388564cf808feff52c16bae297a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad7be678f22aed46fbd0465379fb9e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10ad623f3a05ecdc27b3f3e0169669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e7106619c08f2bcc1d21f846e8a0de.png)
您最近一年使用:0次
7 . 如图所示,已知
是
的直径,
为圆上任意一点,过
的切线分别与过
两点的切线交于
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45987c98a4df7b2a736cc7650da01cf4.png)
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472216219648/1619472216793088/STEM/14dab56eb62f4ffbac5bbd0f1c0c6859.png)
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8 . 如图所示,过圆
外一点
作它的一条切线,切点为
,过
点作直线
垂直于直线
,垂足为
.
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472216219648/1619472216842240/STEM/1da16b8163464d088175e61cd5d8bb4a.png)
(1)证明:
;
(2)
为线段
上一点,直线
垂直于直线
,且交圆
于
点.过
点的切线交直线
于
.证明:
.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2017/1/25/1619472216219648/1619472216842240/STEM/1da16b8163464d088175e61cd5d8bb4a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee1b8f3bb4a294b4cc67154688304f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f52ef170c9bebf83641eaa4b406b69.png)
您最近一年使用:0次
名校
9 . 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
10 . 如图,已知圆
是
的外接圆,
是
边上的高,
是圆
的直径.
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/de6fa6317d364901817490bd3f2571aa.png)
(1)求证:
;
(2)过点
作圆
的切线交
的延长线于点
,若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47d64e7cd6c3179394120d007ff12a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/de6fa6317d364901817490bd3f2571aa.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/f2fa1e4d40994e2e86c45eba0159a68f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/7c22a079c5f945cb925441033bbf1d30.png)
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/0d679278c1b14071a0c0973e3b5ca669.png)
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/0eed3d0155cb4612b71d2d17bf6712e5.png)
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