1 . 如图,以点
为圆心,
为半径作扇形
已知:
点
在
上,且
垂直平分
动点
在线段
上运动(不与点
重合),设
的外心为
,则
的最小值为( )
![](https://img.xkw.com/dksih/QBM/2020/6/15/2485454148624384/2491013219786753/STEM/f41e38b42a9644878901667d07c7198e.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19b1daf2e3960f3d23cca49177ceab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0361f5170e6c806e687db85ead118e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ab3b90f0dcc845a82c6c56596192a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b64ce3dd41d9899054e2ec58b736ac50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b996e05aecd15a1416b8475c73c02c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc14b9e264c42e07e5dbb4503d2dcc79.png)
![](https://img.xkw.com/dksih/QBM/2020/6/15/2485454148624384/2491013219786753/STEM/f41e38b42a9644878901667d07c7198e.png?resizew=168)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5卷引用:2020年河北省九年级适应性训练一模数学试题
2020年河北省九年级适应性训练一模数学试题2020年河北省石家庄市九年级一模数学试题(已下线)【万唯原创】2021年河北面对面-练册-第六章 圆2(已下线)【万唯原创】2021年河北试题研究-练册-第一部分第六章圆2+3(已下线)【万唯原创】2021年河北面对面-第6章圆第2节
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2 . 如图,在菱形ABCD中,对角线AC,BD交于点O,AE⊥BC交CB延长线于点E,CF∥AE交AD延长线于点F.
(1)求证:四边形AECF是矩形;
(2)连接OE,若AE=12,AD=13,则线段OE的长度是 .
(1)求证:四边形AECF是矩形;
(2)连接OE,若AE=12,AD=13,则线段OE的长度是 .
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480469798420480/2481830092726272/STEM/7b920ee993ef4914969b9e96f362a3a5.png?resizew=197)
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2020-06-10更新
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4卷引用:河北省辛集市2019-2020学年八年级下学期期末数学试题
河北省辛集市2019-2020学年八年级下学期期末数学试题2020年辽宁省沈阳市沈河区中考数学一模试题新疆维吾尔自治区乌鲁木齐市新市区实验学校2020-2021学年八年级下学期期末数学试题(已下线)数学(江苏南京B卷)-学易金卷:2022-2023学年八年级下学期期中考前必刷卷
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3 . 如图,将一矩形纸片ABCD沿着虚线EF剪成两个全等的四边形纸片.根据图中标示的长度与角度,求出剪得的四边形纸片中较短的边AE的长是_____ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/4ec72564-658b-4ec0-b170-37e7f014a25d.png?resizew=182)
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4卷引用:2020年北京市顺义区中考数学一模试题
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4 . 如图,矩形ABCD中,AD=4,对角线AC与BD交于点O,OE⊥AC交BC于点E,CE=3,则矩形ABCD的面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/6f93f34f-3151-4f31-a247-b2637d12a5f2.png?resizew=109)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/6f93f34f-3151-4f31-a247-b2637d12a5f2.png?resizew=109)
A.![]() | B.![]() | C.12 | D.32 |
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贵州省遵义市2019年九年级上学期期末数学试题福建省永春第一中学2019-2020学年八年级下学期5月第一次月考数学试题北京市理工大学附属中学分校2019-2020学年八年级下学期期中数学试题江苏省如皋市实验初中2019-2020学年八年级下学期第二次质量检测数学试题(已下线)【万唯原创】2021年河北试题研究-练册-第一部分第五章四边形3+4(已下线)【万唯原创】2021年陕西省面对面-练习册-第一部分第五单元31河南省林州市2021-2022学年八年级下学期期中调研B数学试题河南省新乡市原阳县2021-2022学年八年级下学期第二次月水平测试数学试题
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5 . 如图,在矩形ABCD 中,AE平分∠BAD 交BC于点E,ED=5,EC=3,则矩形的周长为( )
![](https://img.xkw.com/dksih/QBM/2020/5/15/2463335664148480/2463468239339520/STEM/a9697c67-918b-40c6-8d31-e753bcead6c3.png?resizew=142)
![](https://img.xkw.com/dksih/QBM/2020/5/15/2463335664148480/2463468239339520/STEM/a9697c67-918b-40c6-8d31-e753bcead6c3.png?resizew=142)
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4卷引用:黑龙江省哈尔滨市德强学校2019-2020学年八年级下学期期中数学试题
6 . 如图,在长方形
中,
,
,
为
的中点,点
分别在
上,若
,
为等腰直角三角形,则四边形
的面积为( )
![](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/ecf7679c8b4b1e442ce4286d4b0e9c32.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/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5898ecbb5c528fa6cd5844d2133eb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac907579f33c173bf4c710b48db7271f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/a93e0768-ed03-4295-a87c-d60bc3dac705.png?resizew=126)
A.10 | B.9 | C.![]() | D.![]() |
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7 . 如图,O是矩形ABCD的对角线AC的中点,M是AD的中点,若AB=5,AD=12,则四边形ABOM的周长为( )
![](https://img.xkw.com/dksih/QBM/2020/5/4/2455665932640256/2456847619670016/STEM/eda347451f2740ab9f7b5c46d8655aa8.png?resizew=157)
![](https://img.xkw.com/dksih/QBM/2020/5/4/2455665932640256/2456847619670016/STEM/eda347451f2740ab9f7b5c46d8655aa8.png?resizew=157)
A.18 | B.20 | C.22 | D.24 |
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5卷引用:山东省济南市莱芜实验中学 2019-2020学年八年级下学期4月月考数学试题
8 . 如图,矩形
的对角线
,则
的长度是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/25/39949819-b6c8-4840-9a30-661d38d5aec9.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4cc260145b1b6976a7e812dcee4a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/25/39949819-b6c8-4840-9a30-661d38d5aec9.png?resizew=137)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:2019年广西壮族自治区岑溪市中考数学一模试题
2019年广西壮族自治区岑溪市中考数学一模试题(已下线)【万唯原创】矩形、菱形、正方形·满分特训(一)(已下线)【万唯原创】矩 形·满分特训(三) 河北省石家庄市栾城区石门实验学校2022-2023学年九年级上学期开学数学试卷
9 . 已知
是等腰三角形,
,
,点
在边
上,点
在边
上(点
不与所在线段端点重合),
,连接
,射线
,延长
交射线
于点
,点
在直线
上,且
.
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446230046875648/2446433427439616/STEM/e8ea16277d6f44d0a2d1f140f5023c0b.png?resizew=459)
(1)如图,当
时,请直接写出
与
的关系:_____;
与
的位置关系:_____.
(2)当
,其他条件不变时,
的度数是多少?(用含
的代数式表示)
(3)若
是等边三角形,
,
是
边上的三等分点,直线
与直线
交于点
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf833ef47e9d7ec4328cf672e7fadf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8093f8309f82b70b84accebab4247fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1470a8fcbdd2fa9badb34e498d14de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643a6f613aed723eca0fd269cf34db8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d00572a90232e08932317af2a53767.png)
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446230046875648/2446433427439616/STEM/e8ea16277d6f44d0a2d1f140f5023c0b.png?resizew=459)
(1)如图,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f955e5cc9f108de6f3ca01e5eb84c52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db609c0ddcb9af21ddbf443d3e527cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c029e4ab80f8a2080d59ba73841f364f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3e081637bcea5368cc72370bae283b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddad21a6de8f54e65123d274c0098c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
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解题方法
10 . 如图,矩形
中,
,
,点
是
边上一点,连接
,把
沿
折叠,点
落点为
,当
为直角三角形时,
的长为__________ ;在折叠过程中,
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.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/2452627c4f1e58eaa74484d85feccd5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da650ee630c36fd5ce9abb4fb826df7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/c7b80681-6410-4f8a-a3ae-1033006dc1af.jpg?resizew=124)
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