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?
Answers
Steve
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
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