how to find the space of one circle minus the second circle

Question

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.

Answer 1

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 $A=\pi R^2 -2C$