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

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