Question

Circle A has radius 6. Circle B has radius 10. They cross at two points that are 5 apart. What is the overlapping area?

Answer 1

we want the area of a segment of each circle, subtended by a chord of length 5.

A: α = 2 arcsin(2.5/6) = .860
B: β = 2 arcsin(2.5/10) = .506

area is thus

1/2 6^2 (α-sinα) + 1/2 10^2 (β-sin)
= 18(.860 - 5/6) + 50(.506 - 1/2)
= 0.780