Fun Problem: Area of Overlapping circles

[relativitydude]

Picture two indentical circles with their radii overlapping. They form an intersection, what is the area of their intersection?

I solved it the calculus route and it can be solved geometrically. Have fun.

 

[Gokul43201]

Use the cosine rule to find the two subtended angles. From these you can find the areas of the sectors as well as the triagles subtended at the centers. Subtracting, gives the ares of the two caps (segments?). Add these areas to find the area of intersection.

 

[relativitydude]

Please elaborate?