1 . 已知直线m与⊙O,AB是⊙O的直径,AD⊥m于点D.
(1)如图①,当直线m与⊙O相交于点E、F时,求证:∠DAE=∠BAF.
(2)如图②,当直线m与⊙O相切于点C时,若∠DAC=35°,求∠BAC的大小;
(3)若PC=2
,PB=2,求阴影部分的面积(结果保留π).
(1)如图①,当直线m与⊙O相交于点E、F时,求证:∠DAE=∠BAF.
(2)如图②,当直线m与⊙O相切于点C时,若∠DAC=35°,求∠BAC的大小;
(3)若PC=2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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2 . 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)
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3 . 如图,矩形
中,
,
,以A为圆心
为半径作弧与
交于点E,再以C为圆心,
为半径作弧交
于点F,则图中阴影部分的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/98bd8f72-d0b6-4611-9ca7-4f9ca605ef18.png?resizew=148)
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4 . 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)
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真题
5 . 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)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/5873e023-504c-43bd-91c4-bbe29619220a.png?resizew=204)
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6 . 如图,扇形
的半径
厘米,圆心角
,点
是
的中点,点
、
分别是半径
、
上的点,且
.
,
,则图中阴影的面积为______ 平方厘米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2021九年级·全国·专题练习
7 . 如图,已知⊙O的半径为10,A、B是⊙O上的两点,∠AOB=90°,C是射线OB上一个动点,连结AC并延长交⊙O于点D,过点D作DE⊥OD交OB的延长线于点E.当∠A从30°增大到60°时,弦AD在圆内扫过的面积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/bb78ff53-a138-43b5-b620-3bd409256ac9.png?resizew=196)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/bb78ff53-a138-43b5-b620-3bd409256ac9.png?resizew=196)
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8 . 如图,以AB为直径的半圆圆心为O,AB=10,折叠半圆使点A,点B都与圆心O重合,折痕分别为CD,EF,连接DF,则图中阴影的面积为( )
![](https://img.xkw.com/dksih/QBM/2021/5/6/2715145476063232/2717104138682368/STEM/cc489191-ab09-4b59-a2e1-86cbb5d16832.png)
![](https://img.xkw.com/dksih/QBM/2021/5/6/2715145476063232/2717104138682368/STEM/cc489191-ab09-4b59-a2e1-86cbb5d16832.png)
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9 . 如图,在
中,
,
,点
为
上一点,以
为圆心,
长为半径的圆与
相切于点
,交
于另一点
,点
为优弧
上一动点,则图中阴影部分面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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10 . 我们研究过的图形中,圆的任何一对平行切线的距离总是相等的,所以闹息“等宽曲线”.除了圆以外,还有一些几何图形也是“等宽曲线”,如勒洛三角形(如图1),它是分别以等边三角形的每个顶点为圆心,以边长为半径,在另两个顶点间画一段圆弧,三段圆弧围成的曲边三角形.图2是等宽的勒洛三角形和圆形滚木的截面图( )
,则勒洛三角形的周长为
;④图3中,在
中随机以一点,则该点取自勒洛三角形
部分的概率为
,上述结论中,所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129d17c9a49272d44a0e70346414d12d.png)
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