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
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
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