Problem #85
In the figure below, ABCD is a rectangle and ABE
is an isosceles right triangle. The two larger circles are congruent to
each other and are each tangent to two sides of the rectangle, to
triangle ABE, and to the smaller circle. Point E lies on
the smaller circle.

What is the ratio of AB to BC?

What is the ratio of the radius of one of the larger circles to that of
the smaller circle?