I've been wondering if the following has a generalisation, and if so, what is it? I couldn't arrive at a result, partly because the calculation was too much to do and I didn't know in what direction to proceed.
Consider two circles, $ (x-a)² + (y-b)² = c² $ and $ (x-p)² + (y-q)² = r² $. If they intersect, what is the area of their common region? (or, area between the two circles?)
One condition that can be imposed is that the distance between their centres is definitely less than the sum of their radii, only then will they intersect.
How do I proceed from here? Please point me in the right direction, and a detailed solution and explanation would help too. Thanks.