Two overlapping identical circles have radii of 6.17. The area of their overlapping sections is 42.7. How far apart are the centers of the circles?

Answer is 6.55

1 answer

Draw a diagram.

If the intersection points subtend an angle of θ, then the area of overlap is

2*(1/2)r^2(θ-sinθ)
so, you have

6.17^2 (θ-sinθ) = 42.7
θ = 2

The distance between centers is then

2rcos(θ/2) = 2*6.17*cos(1) = 6.67