1 . 选修4-1:几何证明选讲
如图,过点
作圆
的割线
与切线
,
为切点,连接
,
,
的平分线与
,
分别交于点
,
,其中
.
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572031037652992/1572031043420160/STEM/5996f1f3c9e244e0a3d90f4a4bec5612.png)
求证:
;
求
的大小.
如图,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab653ffa6acf8b28096ff54719579d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81574a3738c0a314293ff7c74248971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e701290896a6a607a80c6556e833b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caef922685cef76f1ad8475c29bd04a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ebbd866e455cf80ea669c9f56f792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afa86900c651a7ce4a2a180e06f9008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c065b293986a6728dae546acc0b199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d9ef421906bd73837cdba683037917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afa86900c651a7ce4a2a180e06f9008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c065b293986a6728dae546acc0b199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0b669ef4514f24ee09adeff7f41238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b309a69bd4786e90412a810e8ad0600c.png)
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572031037652992/1572031043420160/STEM/5996f1f3c9e244e0a3d90f4a4bec5612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baca09215d12421a58bd6a48ae16c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd133f93f01cc7cfd566e8aaf7629000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0c12379ff58d8ddf66547d7a873baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea899a0aa6359022562ecf806c9e517e.png)
您最近一年使用:0次
2019-01-30更新
|
256次组卷
|
2卷引用:2015届吉林省长春市普通高中高三质量监测(二)理科数学试卷
2 . 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)
您最近一年使用:0次
名校
3 . 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)
您最近一年使用:0次
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
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
名校
5 . 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
6 . 选修4-1:几何证明选讲:
如右图,圆
与圆
内切于点
,其半径分别为3与2,圆
的弦
交圆
于点
(
不在
上),
是圆
的一条直径.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/0ea025a9-b7c5-440b-8e7c-b79a6983bbd9.png?resizew=187)
(Ⅰ)求
的值;
(Ⅱ)若
,求
到弦
的距离.
如右图,圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/0ea025a9-b7c5-440b-8e7c-b79a6983bbd9.png?resizew=187)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746853ea6d76bd7cccc6bdd6c739aed7.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
7 . 选修4—1:几何证明选讲
如图,正方形
边长为2,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/2015/11/24/1572303048089600/1572303053774848/STEM/2b0f6c30d08f4e0cb3a387d46d38108a.png)
(1)求证:
;
(2)求
的值.
如图,正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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://img.xkw.com/dksih/QBM/2015/11/24/1572303048089600/1572303053774848/STEM/2b0f6c30d08f4e0cb3a387d46d38108a.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572303048089600/1572303053774848/STEM/f517e292c11c41738576ba48ba458eee.png)
(2)求
![](https://img.xkw.com/dksih/QBM/2015/11/24/1572303048089600/1572303053774848/STEM/b8c0ccf4209b4eb19bfe65d27a72052d.png)
您最近一年使用:0次
2016-12-03更新
|
189次组卷
|
4卷引用:2016届宁夏银川一中高三上学期第三次月考理科数学试卷
8 . 如图,
为
外一点,
是切线,
为切点,割线
与
相交于点
,
,且
,
为线段
的中点,
的延长线交
于点
,若
,则![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/f32e92fd1a6c450aa26df035d1269dea.png?resizew=37)
__________ ;![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/4d53185f6bc64ef4a9b578e6b7c1a31d.png?resizew=71)
_________ .
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/1d3753cd3bba4b28839998d4bc815be1.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/a290c5c8df1a42949b9d211ae070148a.png?resizew=25)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/46a2b7435d4649faae6ef43b9e7ed8ba.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/1b4a4d430d2c4df292811eca03a4ea1b.png?resizew=37)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/39dc1386bd7b4f7297765b191b06a438.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/15c513a735ea40f1b29ae719c45e5f32.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/2d62063d16e84187b23d371a12418680.png?resizew=71)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/4de392ecfa0b4bcbba9ca723a52aa735.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/89876b0b808a434fa4643e41e90f63bf.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/0dfdc0d262a84452bf062ba8ce9b2cc9.png?resizew=28)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/3288a2058455442d873cf887579060b3.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4559ab08021b52736d249a6e4424892.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/f32e92fd1a6c450aa26df035d1269dea.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/4d53185f6bc64ef4a9b578e6b7c1a31d.png?resizew=71)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379741696/STEM/2a22a27640444493a2705eae2b7cb50e.png?resizew=171)
您最近一年使用:0次
9 . 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)
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2016-12-03更新
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566次组卷
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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
10 . 选修4—1:几何证明选讲
如图,AB是
的直径,弦BD、CA的延长线相交于点E,F为BA延长线上一点,且
,求证:
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572124333285376/1572124339879936/STEM/6aaa1a8144514f609e6c46244bcb98ca.png)
(1)
;
(2)
.
如图,AB是
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572124333285376/1572124339879936/STEM/0b35f0ca5c7f42499290426caf20727c.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572124333285376/1572124339879936/STEM/043e8b161a544968bf12a2e3696c9d54.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572124333285376/1572124339879936/STEM/6aaa1a8144514f609e6c46244bcb98ca.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43f790457e28ec7a918e4352eaf81df.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990be575bbb0ac644bbb04f23c19ce21.png)
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