Mensa Double Circle Geometry Problem

 

ABCD is a line segment that passes through the centers of two unequal and non-intersecting circles. AB is the diameter of the smaller circle, and CD is the diameter of the larger circle. (Refer to diagram).

Two rays extend from A that are:

1) tangent to the larger circle on opposite sides, and

2) tangent to circle X1 which is inside the smaller circle and touches it at point B.

Likewise two rays extend from A that are:

1) tangent to the smaller circle on opposite sides, and

2) tangent to circle X2 that is inside the larger circle and touches it at point C.

Given this information prove that X1 = X2