如图,等腰三角形ABC中,P为底边BC上任意点,过P作两腰的平行线分别与AB,AC相交于Q,R两点,又P′是P关于直线RQ的对称点,证明:P′在△ABC的外接圆上.
![](https://img.xkw.com/dksih/QBM/2018/8/30/2021615691931648/2023801524985856/STEM/a70fe72561f34a7b821b8ecb4a7f236e.png?resizew=172)
更新时间:2018-09-02 17:37:39
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【知识点】 圆与三角形的综合(圆的综合问题)
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解答题-证明题
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适中
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【推荐1】如图,AB为半圆O的直径,AC是⊙O的一条弦,D为
的中点,作DE⊥AC于点E,交AB的延长线于点F,连结AD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/014b5665-8d2f-4c2c-86cf-7d3d7de296d1.png?resizew=169)
(1)求证:EF为半圆O的切线.
(2)若AO=BF=2,求阴影区域的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/014b5665-8d2f-4c2c-86cf-7d3d7de296d1.png?resizew=169)
(1)求证:EF为半圆O的切线.
(2)若AO=BF=2,求阴影区域的面积.
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解答题-证明题
|
适中
(0.65)
【推荐2】如图,
是
的外接圆,
是
的直径,
是
的切线,切点为F,
,连接
交
于E,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/c0984191-375e-41b0-9154-3494a84149dd.png?resizew=186)
(1)证明:
平分
;
(2)若
的平分线
交
于点D,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f1f880e5ffbff036953acaca90c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d2fbd75defb29e805cb17470cd6133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/c0984191-375e-41b0-9154-3494a84149dd.png?resizew=186)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613dedf2d90e58591b7ac4a250ac7b5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea147ada4f0aefdd3808a6a1133792eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70571e32e85ffbf3db5830136cdbbe44.png)
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