I got two circles c1 and c2 with the same radius and different center. The two circles overlapped. How to calculate the space in C1 without the overlapped section with C2.
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See if this is helpful. – hexaflexagonal Jul 08 '15 at 16:55
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Perhaps this helps: http://math.stackexchange.com/questions/402858/area-of-intersection-between-two-circles – Fluffy12 Jul 08 '15 at 16:56
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I need opposite ! the space on circle one despite of overlapped space with circle 2 – user1658028 Jul 08 '15 at 16:59
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1@user1658028: Simply subtract the area of the intersection from the area of the first circle. – hexaflexagonal Jul 08 '15 at 17:00
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1But to be clear, you cannot use directly the answers to the question @Fluffy12 linked, as that is the specific case where each circle passes through the other's center. – hexaflexagonal Jul 08 '15 at 17:02
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Hint:
If $d$ is the distance between the centers of the two circles (of radius $R$) than the angle at center of one circle that subtend the arc between the common points is : $ \theta=2\arccos(d/2) $
Now use this angle to find the area of the circular segment as $$ C=R^2(\theta -\sin \theta)/2 $$
and the area that you want is $A=\pi R^2 -2C$
Emilio Novati
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Thanks in advance. This is great. Is it also possible to find the same result by using the distance of centers instead of angle calculation? – user1658028 Jul 09 '15 at 03:24
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No. To calculate the area of a circular segment we need the angle. – Emilio Novati Jul 09 '15 at 09:28