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dnaxx

Areas of intersecting circles

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Hello, I want to calculate the intersecting areas 1,2,3 of the four circles as depicted in the following graphic: I know that I learned this in school, but it is too long ago :(. Can you give me some hints? Regards,

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A circular sector is the union of a triangle and a "cap", so you can use the formula for area of a sector and area of a triangle to compute the area of a cap. In your diagram, region 1 is the union of a square and 4 caps. The region formed by 1, 3, and the reflection of 3 through 1 is the union of 2 caps, the caps having the same area. This allows you to compute the area of region 3. The square connecting the circle centers is the union of region 1, 4 regions having area of region 3, and 4 regions having the area of region 2. This allows you to compute the area of region 2.

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thanks, I got the idea.
But one thing remains unclear. How do I get the dimensions of the square that is needed for calculation of region 1? Is there a special ratio between the lengths of (along the big squares diagonal) of section 3-1-3?

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