1 . 如图,
内接于半径为1的
,
,过点A作
,
的延长线交
于点E,交直线
于点D,连接
.
(1)求证:
是
的切线;
(2)若
,求图中阴影部分的面积;
(3)记
的面积为
,
的面积为
,
的面积为
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.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/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/23/7a6da17a-380a-4656-ab29-f5850eb4a3cf.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810242c9205006b28c6bc6612c2b1cd0.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea46133f0ce8a230e503f150955c6d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2657e02314469ad2b13d31dce41b4343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1eef87428af97baf1b0b90c5dfb282b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dd37bdc8ebd0561555e698ee7f1bc6.png)
您最近一年使用:0次
真题
2 . 在学习完《图形的旋转》后,刘老师带领学生开展了一次数学探究活动
【问题情境】
刘老师先引导学生回顾了华东师大版教材七年级下册第
页“探索”部分内容:
如图,将一个三角形纸板
绕点
逆时针旋转
到达
的位置,那么可以得到:
,
,
;
,
,
( )
【问题解决】
(1)上述问题情境中“( )”处应填理由:____________________;
(2)如图,小王将一个半径为
,圆心角为
的扇形纸板
绕点
逆时针旋转
到达扇形纸板
的位置.
;
②如果
,则在旋转过程中,点
经过的路径长为__________;
【问题拓展】
小李突发奇想,将与(2)中完全相同的两个扇形纸板重叠,一个固定在墙上,使得一边位于水平位置,另一个在弧的中点处固定,然后放开纸板,使其摆动到竖直位置时静止,此时,两个纸板重叠部分的面积是多少呢?如图所示,请你帮助小李解决这个问题.
【问题情境】
刘老师先引导学生回顾了华东师大版教材七年级下册第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954a2802eb5dd8d0f92c15cdf0698d57.png)
如图,将一个三角形纸板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c021993da445858448d368df42554c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c2767a255e4eb69916a0dcbf339581b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af33685c34d269c03e0f24393ea4c203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8c6e61bd887fcc69fc2ccd5e57ab03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db82291a3847c98b0844017f6a2af72a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e1abdf6505122e4c5770cc780adce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f937a2ebc35ee7af7ee8782c0ab1828a.png)
【问题解决】
(1)上述问题情境中“( )”处应填理由:____________________;
(2)如图,小王将一个半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf8111bf36bfb6420a734cc51560e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1264a2e3609e1c274acb89b5ea5019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
②如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783e3fa650660d0f4f797d5d237207f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
【问题拓展】
小李突发奇想,将与(2)中完全相同的两个扇形纸板重叠,一个固定在墙上,使得一边位于水平位置,另一个在弧的中点处固定,然后放开纸板,使其摆动到竖直位置时静止,此时,两个纸板重叠部分的面积是多少呢?如图所示,请你帮助小李解决这个问题.
您最近一年使用:0次
2023-06-18更新
|
1184次组卷
|
14卷引用:2023年四川省乐山市中考数学真题
2023年四川省乐山市中考数学真题 (已下线)专题22 几何压轴题-学易金卷:2023年中考数学真题分项汇编(四川专用)(已下线)专题13 三角形基础、全等三角形、等腰三角形和直角三角形-学易金卷:2023年中考数学真题分项汇编(四川专用)(已下线)专题20 平移、轴对称、旋转、中心对称-学易金卷:2023年中考数学真题分项汇编(四川专用)(已下线)专题17 圆的有关概念、性质及计算-学易金卷:2023年中考数学真题分项汇编(四川专用)(已下线)专题19 几何变换(图形的平移、旋转与对称)-学易金卷:三年(2021-2023)中考数学真题分项汇编(四川专用)(已下线)2023四川省乐山市中考数学变式题22-26题31-与圆有关的计算河南省信阳市2023-2024学年九年级上学期期末数学试题山东省德州市庆云县2023-2024学年九年级上学期期末数学试题(已下线)专题5 回顾教材(已下线)重难点05 圆的综合压轴题(6大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(全国通用)(已下线)突破03 函数问题过程性学习探究型-备战2024年中考数学真题题源解密(全国通用)(已下线)重难点07+圆中的计算及其综合2(4考点7题型)
3 . 如图,在
中,
,把
绕点A顺时针旋转,使
落到
延长线上的
处,得到
,点B的对应点为D,点C的对应点为E,旋转过程中得到两条弧
,
,
与
交于点F,连接
.
(1)求
的度数;
(2)若
,求阴影部分的面积;
(3)若
,弧BD与线段
只有一个公共点D,直接写出线段
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c646c683fbe522edb7ea54fd3ad873d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/8192018a58bb1fe23769a48a4d9042ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bf05f26cb828910e47ddb5c8dedd66.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/20/96b53da9-d6ec-4597-a4ec-1ef400004189.png?resizew=162)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384da7acfefa7c656eaca2df173f0cb6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454328a8e75953fdb0835ce80d9566e3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-06-16更新
|
304次组卷
|
5卷引用:2023年河北省石家庄市九地市6月份中考三模数学试题
2023年河北省石家庄市九地市6月份中考三模数学试题(已下线)2023年河北省中考数学真题变式题21-26题河北省邯郸市峰峰矿区2023-2024学年九年级上学期期中数学试题河北省沧州市东光县2023-2024学年九年级上学期期中数学试题(已下线)2023四川省乐山市中考数学变式题22-26题
4 . 在平面内,将小棒
经过适当的运动,使它调转方向(调转前后的小棒不一定在同一条直线上),那么小棒扫过区域的面积如何尽可能地小呢?
已知小棒长度为4,宽度不计.
方案1:将小棒绕
中点O旋转180°到
,设小棒扫过区域的面积为
(即图中灰色区域的面积,下同);
方案2:将小棒先绕A逆时针旋转60°到
,再绕C逆时针旋转60°到
,最后绕B逆时针旋转60°到
,设小棒扫过区域的面积为
.
(1)①
______,
______;(结果保留
)
②比较
与
的大小.(参考数据:
,
.)
(2)方案2可优化为方案3:首次旋转后,将小棒先沿着小棒所在的直线平移再分别进行第2、3次旋转,三次旋转扫过的面积会重叠更多,最终小棒扫过的区域是一个等边三角形.
①补全方案3的示意图;
②设方案3中小棒扫过区域的面积为
,求
.
(3)设计方案4,使小棒扫过区域的面积
小于
,画出示意图并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
已知小棒长度为4,宽度不计.
方案1:将小棒绕
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69596e1040b4b35b7c1e05e2533cc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
方案2:将小棒先绕A逆时针旋转60°到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69596e1040b4b35b7c1e05e2533cc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/29/a12cae96-da4b-4e58-8065-1b8155c20895.png?resizew=529)
(1)①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dabace330ccdd9755fbcf32d5d6343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b625192d7398634a02ea24fa78ed87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
②比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a061dce0c7716ceab53159cd4ce7904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460317e7c26f95b9b29cfe1a89b796d6.png)
(2)方案2可优化为方案3:首次旋转后,将小棒先沿着小棒所在的直线平移再分别进行第2、3次旋转,三次旋转扫过的面积会重叠更多,最终小棒扫过的区域是一个等边三角形.
①补全方案3的示意图;
②设方案3中小棒扫过区域的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
(3)设计方案4,使小棒扫过区域的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
您最近一年使用:0次
5 . 预警三角标志牌用于放置在车道上,告知后方来车前有停置车辆,如图所示
所示
贝贝想制作类似此标志的图形,先使用反光材料设计一个物件,如图
所示,其中四边形
为长方形,
、
分别以
、
为直径的半圆,且灰色部分为反光区域
接着,将三个图
的物件以图
的方式组合并固定,其中固定点
、
、
皆与半圆的圆心重合,且各半圆恰好与长方形的长边相切,而在图
左下方的局部放大图中,
、
皆为其切点,
、
皆为直径.
请根据上述资讯,回答下列问题:
(1)图
中
的度数为多少?
(2)根据图
的组合方式,求出可看见的反光区域面积为多少?请详细解释或完整写出你的解题过程,并求出答案.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](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/6dacb04fa29178c0af4353e4369a7e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/8923a1db-e7a9-4566-97c6-4b1997cef7ee.png?resizew=629)
请根据上述资讯,回答下列问题:
(1)图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a73cccf222ee3fad9c27ef7e7fefc4.png)
(2)根据图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
您最近一年使用:0次
6 . 如图,在正方形
中,以A为圆心,作半径为4的圆心角是
的弧,且这条弧恰好经过B、D两点.
的一条切线与
分别交于M、N.求图中阴影部分面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6612c697aa43a72115e5dce1106c0557.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/30/00c64754-ac67-4d89-97c7-e902a76765ed.png?resizew=188)
您最近一年使用:0次
7 . 如图所示,
中,
,点
在
上,以
为圆心的半圆分别与
相切于
两点,且
的长度为
,则图中的阴影部分面积为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cf90c8a85d9e95cffb7f5c867f8e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833ee84968e2c903b6350c23943b4fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae728c7be0f0cf78711f3fa5ccccf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67fb457e8ac0d3ac35e1c668ea138f91.png)
您最近一年使用:0次
2023-03-28更新
|
259次组卷
|
3卷引用:2023年山东省菏泽市成武县育青中学中考一模数学试题
名校
8 . 某中学开展劳动实习,学生加工制作零件,零件的截面如图所示.O为圆孔及轮廓圆弧
所在圆的圆心,A是圆弧
与直线
的切点,B是圆弧
与直线
的切点,四边形
为矩形,
,垂足为C,
,
,
,
,A到直线
和
的距离均为
,圆孔半径为
,则图中阴影部分的面积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6932dd441452ba74244c828b3fa46ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388a975ada0e731f880a9ea5ca037841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b2332291d454751fa1d7b94fed1251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ada8e9fd2c6d6af8bb0177a07a69c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d1f6a42b01c73543f1e68daf07ef54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfad683e1ec57bac1266e8b0166722b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67f966f8f6705ca3a8916959386eaab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd5d6c0cfb272a71f867751d9d01152.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/3b3c1fd6-b0c4-4502-809f-6ea72dd37f1e.png?resizew=224)
您最近一年使用:0次
2023九年级·全国·专题练习
9 . 滹沱河岸边盛开的粉黛乱子草吸引了很多市民前来观赏,如图1是其中一处美景的俯视图,漂亮的粉黛乱子草(扇形
中的阴影部分)花开灿烂,已知扇形半径
米,
米,点P为
的中点,
上有一座供游人休息的亭子(矩形
),点H,G分别在
上,
在
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/808965fc-1910-407e-80e1-80e7b3c6c313.png?resizew=332)
(1)求粉黛乱子草的种植面积;
(2)爱思考的嘉嘉想:“这个矩形亭子的占地面积能否再大一些呢?”请你通过计算回答嘉嘉的问题;
(3)在点P处垂直于地面向上竖着一根高为
米的柱子
,在A处安装有一个自动喷水装置.水流在各个方向上沿抛物线路径落下,喷出的水流在距离
的水平距离为
米时达到最高点.当喷头A旋转时,整个粉黛乱子草刚好都能被喷出的水流覆盖.建立如图2的坐标系,求出此坐标系中抛物线水流对应的函数关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2935a591c968df92a8cdd2bf09d96452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa1b519e1c71e72fc08e9d8fc8271cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a543ee2e30e27fb47a87a092710a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc869125145c0139d92490a41bd3918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2eac387636cb6acc92331412a59802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24706bdc4f1bd0a9b9291d792850b148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/808965fc-1910-407e-80e1-80e7b3c6c313.png?resizew=332)
(1)求粉黛乱子草的种植面积;
(2)爱思考的嘉嘉想:“这个矩形亭子的占地面积能否再大一些呢?”请你通过计算回答嘉嘉的问题;
(3)在点P处垂直于地面向上竖着一根高为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f3c9b8ef8ee06dc335e5dffa45931c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
您最近一年使用:0次
10 . 如图1,
的半径为
,
的顶点
,
,
在
上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/ae576eca-99dc-4ded-9f64-d0536984e3b4.png?resizew=376)
(1)求证:
是
的切线;
(2)若
也与
相切,求证:四边形
是菱形;
(3)如图2,
与
相交于点
,连接于
,当
时,求
的对角线
的长及阴影部分图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/ae576eca-99dc-4ded-9f64-d0536984e3b4.png?resizew=376)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)如图2,
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51e114946a52a5621d4e9b73165fa28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次