1 . 若一直线与圆相交,过交点作圆的切线,则此切线与直线的夹角称为直线和圆的交角,其中所夹弧为劣弧的角为劣交角,所夹弧为优弧的角为优交角.直线和圆的交角有以下性质:直线和圆的交角等于所夹弧所对的圆周角.
已知:如图1,直线
与
相交于点
,过点
作
的切线
,点
为
上任一点,连接
.求证:
______.
(2)如图2,直线
与
相交于
,
为
的直径,
切
于点
,交
的延长线于点
,若
,
,求
的半径.
已知:如图1,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6d50515fc65885d44cd6a3c41e6a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d715af2d0f55f1f8855361afee3fd0f.png)
(2)如图2,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d2530e7023b2345c651e8f53629ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
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2 . 如图,在边长为6的正方形
中,E是
边上一点,连接
,在
上取一点F,使
,过点F作
交
于点G,若
,
时,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e3d3cc71551dea182cf280ac7c16ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51246bfbcf524ed6da2eceec37712470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f09f62d21a23b48fdd35381ebbd3a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd08bc61b645f7fc10a2add220a0832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
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2024-04-03更新
|
160次组卷
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4卷引用:2023年贵州省贵阳市观山湖区中考模拟数学模拟预测题
2023年贵州省贵阳市观山湖区中考模拟数学模拟预测题2023年贵州省铜仁市第五中学中考数学四模模拟预测题2023学年贵州省铜仁市第五中学九年级下学期第四次模拟数学模拟预测题(已下线)数学(湖北卷)-学易金卷:2024年中考考前押题密卷
3 . 如图,
为
的直径,
是
上一点,过点
的直线交
的延长线于点
,作
,垂足为
,已知
平分
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/8cd4b713-fecc-4633-94b0-3890bb1496fa.png?resizew=178)
(1)求证:
是
的切线;
(2)若
,求
的值.
![](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/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b33dddf09abfbd05cd35683b2b70ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94d2506539ad8760cf7ed366c0c537c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/8cd4b713-fecc-4633-94b0-3890bb1496fa.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe11b3b95c85f5aca6d3de3be942190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8505a97df21a6bb96f4ac9d8817f847a.png)
您最近一年使用:0次
2024-04-03更新
|
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|
2卷引用:2023年贵州省铜仁市沿河县第一教育集团中考数学一模模拟试题
4 . 综合与实践
如图,
是
的切线,
为切点,
是圆上与
不重合的两点.
(1)如图1,若
是
直径,
,则
________.
问题探究
(2)如图2,当
为
上任意一点时,
与
有怎样的关系?并加以证明.
拓展运用
(3)如图3,
的半径是2,
,求
的大小.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0520e9675bc1b416e8b8f01eb69fd13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)如图1,若
![](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/ed09914814b6abbfb04769ca7ca24567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc79fee8f7996b58dbed724fe6afcddb.png)
问题探究
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32986401a4d24904d5e446fa9210ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
拓展运用
(3)如图3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b968d9de81b3730d6b2bb9dba8ed0de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
您最近一年使用:0次
2024-04-03更新
|
64次组卷
|
2卷引用:贵州省遵义市新蒲新区2023年初中生毕业认定测试九年级数学模拟预测题
5 . 探究式学习是新课程倡导的重要学习方式,某兴趣小组拟做以下探究.
在
中,
,
,D是
边上一点,且
(n为正整数),E是
边上的动点,过点D作
的垂线交直线
于点F.
【初步感知】
(1)如图1,当
时,兴趣小组探究得出结论:
,请写出证明过程.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/a57186cb-bf01-45c1-a8e5-dfce5ba356bb.png?resizew=197)
【深入探究】
(2)如图2,当
,且点F在线段
上时,试探究线段
之间的数量关系,请写出结论并证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/d06f3aba-0df2-4bb4-ace0-0b4179366fdd.png?resizew=191)
【拓展运用】
(3)请通过类比、归纳、猜想,探究出线段
之间数量关系的一般结论(直接写出结论,不必证明).
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825671c551cc4593793b40c43d46757a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
【初步感知】
(1)如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36978e392c8df4668ed3f74641febbfe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/a57186cb-bf01-45c1-a8e5-dfce5ba356bb.png?resizew=197)
【深入探究】
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30bf3421adec0637c315309c2ea9a24.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/d06f3aba-0df2-4bb4-ace0-0b4179366fdd.png?resizew=191)
【拓展运用】
(3)请通过类比、归纳、猜想,探究出线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30bf3421adec0637c315309c2ea9a24.png)
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6 . 如图,以点O为位似中心,把
的各边长放大为原来的2倍得到
,下列说法中,错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/1/79277c30-4899-4923-b805-b5ea9efd08b4.png?resizew=195)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/1/79277c30-4899-4923-b805-b5ea9efd08b4.png?resizew=195)
A.![]() | B.![]() |
C.![]() | D.A,O,![]() |
您最近一年使用:0次
7 . 在矩形中,
,
,点
,
分别是边
和
上的动点,且
,连接
,过点
作
,垂足为点
,连接
,则
的最小值为
![](https://img.xkw.com/dksih/QBM/2023/12/26/3397548121120768/3444375591854080/STEM/3392f9106dc546cfb4fa980f66b5f5ec.png?resizew=140)
您最近一年使用:0次
2024-04-01更新
|
227次组卷
|
4卷引用:贵州省遵义市红花岗区2023-2024学年九年级上学期期中数学试题
8 . 如图是以点为圆心,
为直径的圆形纸片,点
在
上,将该圆形纸片沿直线
对折,点
落在
上的点
处(不与点
重合),连接
,
,
.设
与直径
交于点
.若
,则
的值等于
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9 . 如图,已知点
是第一象限内横坐标为
的一个定点,
轴于点
,交直线
于点
.若点
是线段
上的一个动点,
,
,则点
在线段
上运动时,
点不变,
点随之运动,求当点
从点
运动到点
时,点
运动的路径长是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2241bd71e0c20867029e489f9ba655d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cd2a180ae300bbf2388a709e4c28e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d092884e98638f06a767a9a3d8ec00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.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/dad2a36927223bd70f426ba06aea4b45.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/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-30更新
|
118次组卷
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2卷引用:贵州省贵阳市南明区2022-2023学年九年级下学期期中数学试题
名校
10 . 【问题发现】
(1)如图1所示,
和
均为正三角形,B、D、E三点共线.猜想线段
,
之间的数量关系为 ;
;
【类比探究】
(2)如图2所示,
和
均为等腰直角三角形,
,
,
,B、D、E三点共线,线段
、
交于点F.此时,线段
,
之间的数量关系是什么?请写出证明过程并求出
的度数;
【拓展延伸】
(3)如图3所示,在
中,
,
,
,
为
的中位线,将
绕点A顺时针方向旋转,当
所在直线经过点B时,请直接写出
的长.
(1)如图1所示,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cfb5b3f527ff16771f6cb4741f19bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
【类比探究】
(2)如图2所示,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9776aa108071b50b71adf181bbdaf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d00572a90232e08932317af2a53767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6282292819434a8905a212427613fd85.png)
【拓展延伸】
(3)如图3所示,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/16df6934-b217-4f9d-b447-166811b4d1b2.png?resizew=561)
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2024-03-24更新
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18卷引用:2023年贵州省遵义市第十二中学九年级下学期第一次模拟数学试题
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