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

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 (αsinα) + 1/2 10^2 (βsin)
= 18(.860  5/6) + 50(.506  1/2)
= 0.780