Area of the Quadrilateral Formed by the Centres and Points of Intersection of Two Circles
If two circles intersect at two points, the points of intersections and the centres will form a quadrilateral, CAOB in the diagram below.
The quadrilateral is a kite since sides with the same length pair connect.
The area of a kite is
The diagonal AB is given using the cosine rule.
hence
So 
