Area Of Intersection Between Two Circles
So I've had a problem on my mind for most of today, and although I'm sure the answer is quite simple, I can't seem to figure out how to go about doing this.
The question is this: Suppose you had two circles (A and B) of equal size with a radius . If the two circles were arranged such that the circumference of each circle passed through the center of the other, what would be an expression in terms of for the area where the two circles overlap?
Diagram of what I'm talking about is below (A and B are the centers of the circles):
The area I'm looking for being the middle section.
Hints on how to go about finding it, or a direct solution would be much appreciated :V