1 . 如图,四边形
是平行四边形,
是
的直径,点A在
上,
与
相交于点E,连接
,过点C作
的切线交
于点F.
,求
的度数;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2fbaeab3a5eb2e89a9cf94c7b886b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4598486f8c5ac28b1165b76e78105979.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ac03e0b1559d3a64fefe22b807f6f2.png)
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2 . 已知, 如图四边形 内接于
,
是
的直径,
,点
在
的延长线上,
平分
交
延长线于
,交
于
,连接
,
,
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a888959756991f25f93a40894c4d18.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd1bc0388e7fad3e849ca39c67f5034.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8182f6772e304d8ad9f106a29753c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06fc7811f9525e8b8c833746d6af5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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名校
3 . 如图,四边形
内接于
,
弦
,若
,则
的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6d39135a2f8472d66ea00eda3b13ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45723dce96b74f027adcb1a4ecd19db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/1b8b1f11-cfd6-4f2d-87a4-89eb28f281b9.png?resizew=99)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 如图,
是四边形
的外接圆.若
,则
的度数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/6af6763c-de45-4e85-b3d7-5218e55bae7e.png?resizew=148)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d172e210be0f513aabdaaa1112ef1bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/6af6763c-de45-4e85-b3d7-5218e55bae7e.png?resizew=148)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 如图,四边形
内接于
,
,点
是
的中点,连接
,若
,则
的度数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30f6595dd643813b11ad71df61a10dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219f604632bd927bce98fd7ed35f040b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 如图,在
中,
为直径,点
为圆上一点,将劣弧
沿弦
翻折交
于点
(不与
重合),连结
.若
,则
的度数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/81c5c4a6-e8f7-4d1f-80e0-f03c5c016635.jpg?resizew=124)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94c2e12db59e6c8b964b568396a5564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/81c5c4a6-e8f7-4d1f-80e0-f03c5c016635.jpg?resizew=124)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 如图,四边形
内接于
,若四边形
是平行四边形,则
的大小为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/4922e417-9ece-4528-8a8c-3a2f66179983.png?resizew=138)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607543bb9f55b8a141ed2d6cf0e1a20b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3daae8ec60b2b1f7577dee687247cebb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/4922e417-9ece-4528-8a8c-3a2f66179983.png?resizew=138)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 如图,在
中,
,过点A,C的
与
,
分别交于点D,E,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/25/7bb4553b-3193-45f7-b222-4dca7e5676a9.png?resizew=159)
(1)求证
;
(2)延长
,
相交于点P,若
,则
的度数为 °.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/25/7bb4553b-3193-45f7-b222-4dca7e5676a9.png?resizew=159)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce25e95729c34d26e482512d36dd89b1.png)
(2)延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33dcbf1eff7a7d50ba4d9349d4ff1297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
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9 . 阅读材料,解答问题:
关于圆的引理
古希腊数学家、物理学家阿基米德流传于世的数学著作有10余种,下面是《阿基米德全集》的《引理集》中记载的一个命题:
如图1,是
的弦,点C在
上,
于点D,在弦
上取点E,使
,点F是
上的一点,且
连接
,则
.
小颖对这个问题很感兴趣,经过思考,写出了下面的证明过程:
证明:如图2,连接,
∵于点D,
,
∴ .
∴ .
∵,
∴ (依据1),
.
∵ 四边形内接于
,
∴ .(依据2)
……
(1)上述证明过程中的依据1为_________,依据2为_________;
(2)将上述证明过程补充完整.
您最近一年使用:0次
2023-11-27更新
|
51次组卷
|
9卷引用:2023年山西省长治市襄垣县中考一模数学试卷
2023年山西省长治市襄垣县中考一模数学试卷2023年河南省济源市中考二模数学试题山西省长治市2022-2023学年九年级上学期期末数学试题(已下线)2023年山西一模(阅读思考题综合)(已下线)专题2.4 圆周角、圆内接四边形【十大题型】-2023-2024学年九年级数学上册举一反三系列(苏科版)(已下线)专题3.5 圆周角、圆内接四边形【十大题型】-2023-2024学年九年级数学上册举一反三系列(浙教版)(已下线)专题24.4 圆周角、圆内接四边形【十大题型】-2023-2024学年九年级数学上册举一反三系列(人教版)山西省朔州市多校联考2023-2024学年九年级上学期期中数学试题河南省信阳市息县2023-2024学年九年级上学期期中数学试题
20-21九年级下·全国·课后作业
10 . 已知:如图,在
中,
,以
为直径的
与
交于点D,与
交于点E.
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833513464651776/2842115138330624/STEM/726d3d8d-1ffd-4671-8be4-498a7232a871.png?resizew=213)
求证:
为等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833513464651776/2842115138330624/STEM/726d3d8d-1ffd-4671-8be4-498a7232a871.png?resizew=213)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
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