Asked by jojo
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
Answer is 6.55
Answers
Answered by
Steve
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
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