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Two circles with radii 5 intersect such that the center of one circle lies on the circumference of another. What is the area of the overlapping region in terms of pi?
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Do you know what shape the intersecting circle-edge points form with either of the circle centers? – abiessu Oct 04 '13 at 01:49
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If you were allowed, I just computed an appropriate integration to get $50 \left(\frac{\pi}{3}-\frac{\sqrt{3}}{4} \right) \approx 30.7092$ for comparison at least. Total area of one circle being about 78.5398, and a bit more than twice the desired area, my solution seems pretty feasible. – J. W. Perry Oct 04 '13 at 02:55
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Note that on that link Area of intersection between two circles, the geometric answer by Ilya Melamed corresponds to my calculus. He says $r^2\left( \frac{2\pi}{3}-\frac{\sqrt{3}}{2} \right)$, and that corresponds to my integral. – J. W. Perry Oct 04 '13 at 03:18