31-与圆有关的计算
一、单选题
单选题
|
较难(0.4)
如图,点A,B是半径为2的
上的两点,且
.下列说法错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/6dae8074-3f80-47ad-847b-7bab055f6cc1.png?resizew=109)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/6dae8074-3f80-47ad-847b-7bab055f6cc1.png?resizew=109)
A.圆心O到![]() |
B.在圆上取异于A,B的一点C,则![]() ![]() |
C.以![]() ![]() ![]() ![]() |
D.取弦![]() ![]() ![]() |
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2卷引用:安徽省阜阳市颍州区2023-2024学年九年级上学期期末数学试题
单选题
|
较难(0.4)
如图,在平面直角坐标系中,
,以点A为圆心,OA长为半径作圆,交x轴正半轴于点C,点D为
上一动点,连接BD,以BD为边,在直线BD的上方作正方形BDEF,若点D从点O出发,按顺时针方向以每秒
个单位长度的速度在
上运动,则第2022秒结束时,点F的坐标为( )
![](https://img.xkw.com/dksih/QBM/2022/4/15/2958595551428608/2962421416738816/STEM/3016f74f-3ee0-49b0-ae92-0e2b46add98f.png?resizew=194)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45957d547315c5fead71ca0dd6ff5ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://img.xkw.com/dksih/QBM/2022/4/15/2958595551428608/2962421416738816/STEM/3016f74f-3ee0-49b0-ae92-0e2b46add98f.png?resizew=194)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022年河南省多校中考模拟测评(二)数学试题(已下线)江苏南京卷B-2022年中考数学模拟考场仿真演练卷江苏省泰州市兴化市西南片学校2022-2023学年九年级上学期期末数学试题江苏省泰州市兴化市板桥初级中学2022-2023学年九年级期末数学试题(已下线)24.4 弧长和扇形面积-2022-2023学年九年级数学上册课后培优分级练(人教版)31-与圆有关的计算
单选题
|
较难(0.4)
现在很多家庭都使用折叠型餐桌来节省空间,两边翻开后成为圆形桌面如图①,餐桌两边
和
平行且相等,
如图②,小华用皮尺量得
,
,那么桌面翻成圆桌后,桌子面积会增加( )
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ec180a4e5f7b60d799b4014d5cc33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d52efe8c7ec20d78aa911c0fb90368.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:辽宁省铁岭市2023-2024学年九年级上学期期末数学试题
辽宁省铁岭市2023-2024学年九年级上学期期末数学试题辽宁省铁岭市铁岭县2023-2024学年九年级上学期期末数学试题(已下线)数学(山西卷)-学易金卷:2024年中考考前押题密卷31-与圆有关的计算
单选题
|
较难(0.4)
名校
如图,在矩形
中,
,点
是
边上的一个动点,连接
,点
关于直线
的对称点为
,当点
运动时,点
也随之运动.若点
从点
运动到点
,则线段
扫过的区域的面积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/2906112e-8b00-4579-9771-c3b4c80a6012.png?resizew=179)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1cf954378eca1e0383020c48bbf905c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/2906112e-8b00-4579-9771-c3b4c80a6012.png?resizew=179)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:江苏省无锡市梁溪区东林中学2023-2024学年九年级上学期期中数学试题
单选题
|
较难(0.4)
真题
名校
如图,平面图形
由直角边长为1的等腰直角
和扇形
组成,点
在线段
上,
,且
交
或交
于点
.设
,图中阴影部分表示的平面图形
(或
)的面积为
,则函数
关于
的大致图象是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/54244bf8-9b57-47d6-bf1e-7ae82f53aa9d.png?resizew=209)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372629a8666de1e9bac3e7daadcac7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564743a1fe463a981f06914e3cb5e03e.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/d84733f9dc908ceb11459cc2aed580ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b758913f0b039bba68f657380e1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a0e9106eaf6c2bb11ed6e0a97181f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1de7da3ab92e70f135ea628a691167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bddc68ed03fe7fd1fe30a5e626ba435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/54244bf8-9b57-47d6-bf1e-7ae82f53aa9d.png?resizew=209)
A.![]() | B.![]() | C.![]() | D.![]() |
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9卷引用:2021年山东省日照市中考真题数学试卷
2021年山东省日照市中考真题数学试卷(已下线)押江苏南京中考数学第6题(规律探究、图形变化、几何与函数综合)-备战2022年中考数学临考题号押题(江苏南京专用)2022年宁夏石嘴山市平罗县初中学业水平模拟(一)数学试题2022年江苏省苏州新区实验初中九年级数学三模试题河南省信阳市浉河区浉河中学2021-2022学年九年级上学期10月月考数学试题(已下线)2022年河南省济源市九年级中考第一次模拟考试数学试题变式题6-10(已下线)2022年江苏省南通启东市九年级中考二模数学试题变式题6-10江苏省苏州市苏州中学校2023-2024学年九年级上学期10月月考数学试题31-与圆有关的计算
单选题
|
较难(0.4)
真题
如图,在菱形
中,
,
,以
为圆心、
长为半径画
,点
为菱形内一点,连接
,
,
.当
为等腰直角三角形时,图中阴影部分的面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/5873e023-504c-43bd-91c4-bbe29619220a.png?resizew=204)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4d00b86b2f067b902baf6e52f0faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4234cf4d8159f5df0333bcc269ffe099.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/5873e023-504c-43bd-91c4-bbe29619220a.png?resizew=204)
A.![]() | B.![]() | C.![]() | D.![]() |
【知识点】 求其他不规则图形的面积 三角函数综合
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5卷引用:湖北省荆州市2021年中考数学真题
湖北省荆州市2021年中考数学真题(已下线)2022年湖北省荆州市中考数学真题变式题6-10题广东省台山市育英中学2021-2022学年九年级上学期第三次月考数学试题湖北省天门市华斯达学校2021-2022学年九年级下学期月考数学试题31-与圆有关的计算
单选题
|
较难(0.4)
如图,菱形
的边长为
,
,点
为
边的中点.点
从点
出发,以每秒
个单位的速度向点
运动,点
同时从点
出发,以每秒
个单位的速度向点
运动,连接
,过点
作
于点
.当点
到达点
时,点
也停止运动,则点
的运动路径长是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/28068b45-4b93-4a3d-9950-b6575e9b3dc2.png?resizew=227)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32436704a722d5e568ff5c175bf3c662.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff30e155c09e316411d9b5eaabad815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/28068b45-4b93-4a3d-9950-b6575e9b3dc2.png?resizew=227)
A.![]() | B.12 | C.![]() | D.![]() |
您最近一年使用:0次
单选题
|
较难(0.4)
名校
如图,在
中,
,
,点O是边
的中点,半圆O与
相切于点D、E,若阴影部分的面积为
,则
的长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/5c6a2871-6384-41e7-95aa-1c4126d77d5f.png?resizew=245)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbe15da3f402bccc5ff4b8f8b6d61a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1816fb0bed72025e79aa4b7185055ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9303b41310b6bf2a5fe9b66dfcd7fcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/5c6a2871-6384-41e7-95aa-1c4126d77d5f.png?resizew=245)
A.![]() | B.![]() | C.2 | D.![]() |
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3卷引用:新疆维吾尔自治区乌鲁木齐市第七十中学2021-2022学年九年级上学期期末数学试题
单选题
|
较难(0.4)
您最近一年使用:0次
2023-06-07更新
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413次组卷
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6卷引用: 2023年山东省临沂市河东区中考二模数学试题
2023年山东省临沂市河东区中考二模数学试题新疆维吾尔自治区乌鲁木齐市第二中学2023-2024学年九年级上学期期末数学试题(已下线)2024年四川省广安市中考数学真题变式题6-10题(已下线)专题2.52 圆(全章分层练习)(培优练)-2023-2024学年九年级数学上册基础知识专项突破讲与练(苏科版)(已下线)专题24.41 圆(全章分层练习)(培优练)-2023-2024学年九年级数学上册基础知识专项突破讲与练(人教版)31-与圆有关的计算
单选题
|
较难(0.4)
如图,等边
内接于⊙
,
是
上任一点(不与
、
重合),连接
、
,
交
于
,
切⊙
于点
,
交⊙
于点
.下列结论:①
;②
;③若
,则四边形
的面积为
;④若
,则图中阴影部分的面积为
.正确的个数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/7a5a05a2-01b1-4472-a1ec-d307143c1bbd.png?resizew=184)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/ed41d321f4c0717ac5b443aad942d9a7.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.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/b3b2e39685f8fcf4ce519cf5233a4d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4079e8de6d9b2c82f086c2fc4de6e93e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0524c3287106a4460858ed3926989a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18bf02afcbc78a5c9f50c4633601e69f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/7a5a05a2-01b1-4472-a1ec-d307143c1bbd.png?resizew=184)
A.1个 | B.2个 | C.3个 | D.4个 |
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2卷引用:江苏省无锡市江阴市2021-2022学年九年级上学期期中数学试题
二、填空题
填空题
|
较难(0.4)
解题方法
如图,A,C是双曲线
上关于原点对称的点,B,D是双曲线
上关于原点对称的点,圆弧
与
围成了一个封闭图形,当线段AC与BD都最短时,图中阴影部分的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8684443809254c64330bb349b473bda5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886c57cf5dca1b3f19556111f9284812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc14264fa26d6953bebbf75be2391f6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/6/52514d65-9a07-4f43-80fd-33a555c9638e.png?resizew=175)
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2021-06-06更新
|
3702次组卷
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5卷引用:2021年四川省成都市青白江区中考二诊检测数学试题
2021年四川省成都市青白江区中考二诊检测数学试题(已下线)押四川卷22题 反比例函数与几何综合-备战2022年中考数学临考题号押题(四川专用)(已下线)(专题)圆中不规则图形面积解法(已下线)第26章 反比例函数(基础、常考、易错、压轴)分类专项训练-2022-2023学年九年级数学考试满分全攻略(人教版)31-与圆有关的计算
填空题
|
困难(0.15)
名校
如图,扇形
,且
,
,
为弧
上任意一点,过
点作
于点
,设
的内心为
,连接
、
,当点
从点
运动到点A时,内心
所经过的路径长为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898a3297d89d0702649e61cb5b0c9d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786080c82db1e1d3ec6367397aa63220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f43dd27150098f6dfabfdac92da27e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/53a46442-9b80-4165-9ba8-cfa4ae830e28.png?resizew=157)
【知识点】 求某点的弧形运动路径长度解读
您最近一年使用:0次
2022-11-20更新
|
398次组卷
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2卷引用:江苏省宿迁市沭阳县怀文中学2022-2023学年九年级上学期10月月考数学试题
填空题
|
较难(0.4)
在
中,
,
,
.若点P在
内部(含边界)且
,则所有满足条件的P组成的区域的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073687c90d17116abc086bf50ea61874.png)
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2022-06-22更新
|
468次组卷
|
6卷引用:2022年江苏省南京市鼓楼区中考二模数学试题
2022年江苏省南京市鼓楼区中考二模数学试题江苏省扬州市梅岭教育集团2022-2023学年九年级上学期第三次月考试题江苏省扬州市梅岭中学2022-2023学年九年级上学期第二次月考数学试题(已下线)2022年江苏省南京市鼓楼区中考二模数学试题变式题16-20(已下线)黄金卷05-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷(江苏南京专用)31-与圆有关的计算
填空题
|
较难(0.4)
名校
图1是一款带毛刷的圆型扫地机器人,它的俯视图如图2所示,
的直径为40cm,毛刷的一端为固定点
,另一端为点
,
,毛刷绕着点
旋转形成的圆弧交
于点A,
,且A,
,
三点在同一直线上.毛刷在旋转过程中,与
交于点
,则
的最大长度为______ cm.扫地机器人在遇到障碍物时会自转,毛刷碰到障碍物时可弯曲.如图3,当扫地机器人在清扫角度为60°的墙角(
)时,不能清扫到的面积(图中阴影部分)为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1099613ccab9e6ffbe3ba8ce160f3353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45724e8b0d34b283c6f18f45d13972a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/13/2978501969453056/2979868483141632/STEM/6a74e628-24ed-465c-b960-9a2fab8f94b2.png?resizew=522)
您最近一年使用:0次
2022-05-15更新
|
343次组卷
|
2卷引用:2022年浙江省温州市绣山中学等两校九年级下学期第二次学业水平检测数学试题
填空题
|
较难(0.4)
如图,在半径为2
,圆心角为90°的扇形
中,
,点D是半径
的中点,点E从点D出发,沿
的方向运动到A的过程中,线段
、
与
所围成的区域(图中阴影部分)面积的最小值为____________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099943024568222c20cf16ede1af66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52dedf673f34019d6d7de1b5c86eb29b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/11/12a4f792-800d-4578-8c32-9d9993f88ec9.png?resizew=151)
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3卷引用:2022年福建省泉州市惠安县初中毕业班质量检测数学试题
2022年福建省泉州市惠安县初中毕业班质量检测数学试题(已下线)专题4.5 多边形与圆的认识(能力提升)-2022-2023学年七年级数学上册《同步考点解读·专题训练》(北师大版)31-与圆有关的计算
填空题
|
较难(0.4)
如图,半径为20cm的圆形扫地机器人在无障碍的Rt△ABC房间中自由移动打扫卫生,已知∠B=90°,AB=4m,BC=3m,则圆形扫地机器人无法打扫 到的房间面积为_________ .(结果保留π)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/17/cc6f6b0c-2c36-4e0d-a286-9a5261b438fe.png?resizew=259)
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|
315次组卷
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3卷引用:2022学年江苏省苏州市九年级下学期数学学业质量调研试题
三、解答题
在几何体表面上,蚂蚁怎样爬行路径最短?
(1)如图①,圆锥的母线长为
,B为母线
的中点,点A在底面圆周上,
的长为
.在图②所示的圆锥的侧面展开图中画出蚂蚁从点A爬行到点B的最短路径,并标出它的长(结果保留根号).
![](https://img.xkw.com/dksih/QBM/2021/6/23/2749029562376192/2749069355147264/STEM/5f9bf300-3279-4d2d-9278-7ebb9a19461a.png)
![](https://img.xkw.com/dksih/QBM/2021/6/23/2749029562376192/2749069355147264/STEM/9504ecdd-0ed1-41d3-a32d-2438f05342b4.png)
(2)图③中的几何体由底面半径相同的圆锥和圆柱组成.O是圆锥的顶点,点A在圆柱的底面圆周上.设圆锥的母线长为l,圆柱的高为h.
①蚂蚁从点A爬行到点O的最短路径的长为________(用含l,h的代数式表示).
②设
的长为a,点B在母线
上,
.圆柱的侧面展开图如图④所示,在图中画出蚂蚁从点A爬行到点B的最短路径的示意图,并写出求最短路径的长的思路.
![](https://img.xkw.com/dksih/QBM/2021/6/23/2749029562376192/2749069355147264/STEM/4e2e0a65-f35b-4e39-a089-b7904cd050a3.png)
(1)如图①,圆锥的母线长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc6a8e3c0184a6f39ba69966efee510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf96412cabd4ead64e7fed36c90d9ec.png)
![](https://img.xkw.com/dksih/QBM/2021/6/23/2749029562376192/2749069355147264/STEM/5f9bf300-3279-4d2d-9278-7ebb9a19461a.png)
![](https://img.xkw.com/dksih/QBM/2021/6/23/2749029562376192/2749069355147264/STEM/9504ecdd-0ed1-41d3-a32d-2438f05342b4.png)
(2)图③中的几何体由底面半径相同的圆锥和圆柱组成.O是圆锥的顶点,点A在圆柱的底面圆周上.设圆锥的母线长为l,圆柱的高为h.
①蚂蚁从点A爬行到点O的最短路径的长为________(用含l,h的代数式表示).
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f9353ca110c8b81561455b232dbc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d90bc7fd910d69984c0e271b916563.png)
![](https://img.xkw.com/dksih/QBM/2021/6/23/2749029562376192/2749069355147264/STEM/4e2e0a65-f35b-4e39-a089-b7904cd050a3.png)
![](https://img.xkw.com/dksih/QBM/2021/6/23/2749029562376192/2749069355147264/STEM/21823859-b3f5-4c13-8d36-7552c2d1762f.png)
您最近一年使用:0次
2021-06-23更新
|
2666次组卷
|
6卷引用:江苏省南京市2021年中考数学试卷
江苏省南京市2021年中考数学试卷2022年广东省潮州市湘桥区城南中英文学校中考第一次模拟数学卷(已下线)押江苏南京中考数学第27题(几何综合与探究)-备战2022年中考数学临考题号押题(江苏南京专用)(已下线)专题15 三角形解答题-三年(2020-2022)中考数学真题分项汇编(江苏专用)(已下线)专题19 圆解答题-三年(2020-2022)中考数学真题分项汇编(江苏专用)31-与圆有关的计算
解答题-问答题
|
困难(0.15)
解题方法
已知,在半圆
中,直径
,点
,
在半圆
上运动,(点
,
可以与
,
两点重合),弦
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/20/10e66936-96f8-4416-a052-b4224813f2d2.png?resizew=468)
(1)如图1,当
时,直接写出图中标注顶点的所有全等三角形;
(2)如图2,若
时,求图中阴影部分(弦AD、直径AB、弧BD围成的(图形)的面积;
(3)如图3,取CD的中点
,点
从点
开始运动到点
与点
重合时结束,在整个运动过程中:
①点M到AB的距离的最小值是______;
②直接写出点M的运动路径长______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/55c24a968c73e960698a572ab01e3698.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/20/10e66936-96f8-4416-a052-b4224813f2d2.png?resizew=468)
(1)如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f7abf31402fcfd6f86fb434adc37d1.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e08c088f4281baf6c431ca4ee1fa0a.png)
(3)如图3,取CD的中点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①点M到AB的距离的最小值是______;
②直接写出点M的运动路径长______.
您最近一年使用:0次
2022-06-18更新
|
715次组卷
|
4卷引用:2022年河北省唐山市路南区中考三模数学试题
2022年河北省唐山市路南区中考三模数学试题(已下线)2022年河北省中考数学变式题22-26(已下线)专题06 圆-5年(2018-2022)中考1年模拟数学真题分项汇编(河北专用)31-与圆有关的计算
解答题-作图题
|
较难(0.4)
真题
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31-与圆有关的计算(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)
解答题-问答题
|
较难(0.4)
名校
如图1,四边形
是正方形,且
,点
与点
重合,以
为圆心,作半径长为3的半圆
,交
于点
,交
于点
,交
的延长线于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/d688187f-da05-4658-9ca0-f8873443c7c7.png?resizew=569)
(1)发现:
是半圆
上任意一点,连接
,则
的最大值为_________.
(2)思考:将半圆
绕点
逆时针旋转,记旋转角为
.
如图2,若半圆
直径
经过点
时,求点
转过的弧长.
(3)在旋转过程中圆心
到
和
的距离相等时,求
.
(4)探究:在旋转过程中,若半圆
与正方形的边相切,求点
到切点的距离.
(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/d688187f-da05-4658-9ca0-f8873443c7c7.png?resizew=569)
(1)发现:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(2)思考:将半圆
![](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/05df5a26c2b978503e93efa040b99508.png)
如图2,若半圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(3)在旋转过程中圆心
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f4ce8808384417be24e85762222769.png)
(4)探究:在旋转过程中,若半圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a394e77dac85a8afeb80f12509281dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e1640dd5b7a054089d172a5f8480f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4ac6563e0b4684f01f738d2b71bfd3.png)
您最近一年使用:0次
2022-06-26更新
|
497次组卷
|
6卷引用:2022年河北省廊坊市固安县初中毕业升学模拟考试数学试卷(模拟二)
2022年河北省廊坊市固安县初中毕业升学模拟考试数学试卷(模拟二)(已下线)黄金卷02-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷(河北专用)(已下线)数学(河北卷)-学易金卷:2023年中考考前押题密卷(含考试版、全解全析、参考答案、答题卡)2023年广东省深圳市桂园中学中考模拟数学试题(已下线)2022年河北中考数学二模圆的综合题31-与圆有关的计算
解答题-问答题
|
较难(0.4)
有一张半径为2的圆形纸片.
(1)如图(1),先将纸片沿直径左右翻折,再上下翻折,刚好完全重合,然后平铺展开,则
的大小是 ;在
上任取 点
异于
,
,则
的大小是 ;
(2)如图(2),将纸片沿一条弦
翻折,使其劣弧
恰好经过圆心
,作出直径
,则图中阴影部分的面积是 ;
(3)如图(3),
是
的直径,将劣弧
沿弦
翻折,交
于点
,再将劣弧
沿直径
翻折,交
于点
.若点
恰好是翻折后的劣弧
的中点,求图中阴影部分的面积.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/29f6b2f7-6e0f-4e53-97b3-f81f01efe89c.png?resizew=788)
(1)如图(1),先将纸片沿直径左右翻折,再上下翻折,刚好完全重合,然后平铺展开,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664cc63a58f1b2e0b94d2cae5c6ba5de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d42497ffa5ae82e6d8092db948f4ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32e4b17ab3892d0f5f84a8b4c848357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b664f3a011a2f1f31c66a2635c5367c.png)
(2)如图(2),将纸片沿一条弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
(3)如图(3),
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
您最近一年使用:0次
解答题-问答题
|
较难(0.4)
如图1,扇形OAB的半径为12,∠AOB=90°,P是半径OB上一动点,Q是弧AB上的一动点.连接PQ.
(1)当
度时,
有最大值,最大值为___________;
(2)如图2,若
是
中点,且
于点
.则
的长为
;(结果保留
)
(3)如图3,将图形
沿折痕
折叠,使点
的对应点
恰好落在
的延长线上,求阴影部分面积.(结果保留
)
(4)如图4,将扇形
沿
折叠,使折叠后的
与半径
相交与
、
两点.若
,求
的长.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/6c956415-6e35-4b1d-9ced-02aa93461677.png?resizew=584)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40026e2a2abea494be587171a6f2ac13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62e8aadaadebf1454fde21a390ebdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259e225df354d605e05372a0fd5ce033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a04dba3e66ee26e57fb0039ef779ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fb32a03264151340401a243118d973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2d1ecae9c649cc3c89f9ce0c063208.png)
(3)如图3,将图形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571f8dfb1eb003438f27bab2324140ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e37b122a7273e1251ea3860e74c896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2d1ecae9c649cc3c89f9ce0c063208.png)
(4)如图4,将扇形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a44aa6beb0b8948618d252e7b765de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae36314ca69c5f6572d7d2922647ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d08196b8516e5a5f47b230de813fb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
您最近一年使用:0次
2023-10-30更新
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123次组卷
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2卷引用:江苏省盐城市盐都区鹿鸣路初级中学2023-2024学年九年级上学期第一次月考数学试题
解答题-证明题
|
较难(0.4)
名校
【阅读材料】
请运用上述阅读材料中获取的经验和方法解决下列问题.
【基础应用】已知
中,
,点
在边
上,点
在边
的延长线上,连接
交
于点
.
(1)如图1,若
,
,求证:点
是
的中点;
(2)如图2,若
,
,探究
与
之间的数量关系;
【灵活应用】如图3,
是半圆
的直径,点
是半圆上一点,点
是
上一点,点
在
延长线上,
,
,
,当点
从点
运动到点
,点
运动的路径长为______,
扫过的面积为______.
教材习题 | 如图,![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
问题分析 | 由条件易证![]() ![]() ![]() ![]() | |
方法提取 | 构造“平行![]() |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/18/27a43022-f8bb-4643-b6a5-bcba9a03429f.png?resizew=534)
请运用上述阅读材料中获取的经验和方法解决下列问题.
【基础应用】已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce1475f537b4ad21775bfaa16daa0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5181b97a7e43959b8455680157c3b644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8fe122a768a4d78b5b39817d557a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
【灵活应用】如图3,
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f70794c05487973e77dd74ba48793a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
2023-06-16更新
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544次组卷
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5卷引用:2023年江苏省扬州中学教育集团树人学校中考二模数学试题