Angles in the Quadrilateral Formed By Centres and Intersections of Two Circles
Two circles of raddi R and r respectively. Intersect in the point A and B as shown below.
From the Cosine Rule, for the triangle CAB,and for the triangle OAB,
Setting these equal gives
Now use the identity cos 2x = 1-2 sin^2 x rearranged asto give
Dividing by 4 and square rooting gives