let-s-say-there-are-two-circles-with-their-centers-A1-and-A2-and-their-radii-are-equal-to-r1-and-r2-let-n-be-the-distance-between-the-centers-of-the-two-circles-and-n-r1-r2-Is-there-a-way-to-find-h

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Question Number 215774 by Engr_Jidda last updated on 17/Jan/25

$$ \\ $$let's say there are two circles with their centers A1 and A2 and their radii are equal to r1 and r2 ,let n be the distance between the centers of the two circles and n<r1+r2. Is there a way to find how much is the area that is formed when the two circles are overlapping ?

Answered by AntonCWX last updated on 18/Jan/25

Commented by AntonCWX last updated on 18/Jan/25

Both α and β are in radian Red Region Area =(r_1 )^2 (α−sin(((180α)/π))) Blue Region Area =(r_2 )^2 (β−sin(((180β)/π))) Total area =r_1 ^2 (α−sin(((180α)/π)))+r_2 ^2 (β−sin(((180β)/π)))

$${Both}\:\alpha\:{and}\:\beta\:{are}\:{in}\:{radian} \\ $$$$ \\ $$$${Red}\:{Region}\:{Area} \\ $$$$=\left({r}_{\mathrm{1}} \right)^{\mathrm{2}} \left(\alpha−{sin}\left(\frac{\mathrm{180}\alpha}{\pi}\right)\right) \\ $$$$ \\ $$$${Blue}\:{Region}\:{Area} \\ $$$$=\left({r}_{\mathrm{2}} \right)^{\mathrm{2}} \left(\beta−{sin}\left(\frac{\mathrm{180}\beta}{\pi}\right)\right) \\ $$$$ \\ $$$${Total}\:{area} \\ $$$$={r}_{\mathrm{1}} ^{\mathrm{2}} \left(\alpha−{sin}\left(\frac{\mathrm{180}\alpha}{\pi}\right)\right)+{r}_{\mathrm{2}} ^{\mathrm{2}} \left(\beta−{sin}\left(\frac{\mathrm{180}\beta}{\pi}\right)\right) \\ $$

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let-s-say-there-are-two-circles-with-their-centers-A1-and-A2-and-their-radii-are-equal-to-r1-and-r2-let-n-be-the-distance-between-the-centers-of-the-two-circles-and-n-r1-r2-Is-there-a-way-to-find-h

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