配套习题- 运用转化思想求与圆有关的阴影面积 -【青果学院】

1/5单选题

难度：

1.

如图，以等腰直角△ABC两锐角顶点A、B为圆心作等圆，⊙A与⊙B恰好外切，若AC=2，那么图中两个扇形（即阴影部分）的面积之和为（　　）

A
B
C
D

正确答案：Qg==

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

2/5单选题

难度：

2.如图，以AD为直径的半圆O经过Rt△ABC斜边AB的两个端点，交直角边AC于点E，B、E是半圆弧的三等分点，弧BE的长为

π，则图中阴影部分的面积为()

A
B
C
D

正确答案：RA==

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

3/5单选题

难度：

3.

如图，AB，CD是⊙O的两条互相垂直的直径，点O₁，O₂，O₃，O₄分别是OA、OB、OC、OD的中点，若⊙O的半径为2，则阴影部分的面积为( )

A	8
B	4
C	4n+4
D	4n-4

正确答案：QQ==

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

4/5单选题

难度：

4.如图，将含60°角的直角三角板ABC绕顶点A顺时针旋转45°度后得到△AB′C′，点B经过的路径为弧BB′，若∠BAC=60°，AC=1，则图中阴影部分的面积是（　　）

A
B
C
D

正确答案：QQ==

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

5/5单选题

难度：

5.如图，正方形ABCD中，分别以B、D为圆心，以正方形的边长a为半径画弧，形成树叶形（阴影部分）图案，则树叶形图案的面积为（　　）

A
B
C
D

正确答案：Qw==

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