Question

ABCD is rectangle. BC = 45. Two circles are drawn inside ABCD such that the circles are

tangent to each other. The circle with radius 10 is tangent to AB¯

and BC¯

, and the circle with

radius 15 is tangent to AD¯

and CD¯

. Find AB.​

Answer 1

ABCD is a rectangle. Two circles are drawn inside ABCD such that the circles are tangent at point G. E is the tangent point of the first circle and AB, and F is the tangent point of the second circle and BC, as shown. From center B a tangent is drawn to circle A intersecting the circle at C.