Two circles, whose radii are 12 inches and 16 inches respectively, intersect. The angle between the tangents at either of the points of intersection is 29'30'. Find the distance between the centers of the circles.

Answer 1

poke around a bit and you will find proofs that if the tangents intersect at an angle θ, then if the circles have radii r and R, and the centers are d apart, then

sinθ = √(2r^2R^2 + 2r^2d^2 + 2R^2d^2 - r^4 - R^4 - d^4)/(2Rr)

so, plug in your numbers