AHSME 1974 Problem 16

A circle of radius $r$ is inscribed in a right isosceles triangle, and a circle of radius $R$ is circumscribed about the triangle. Then $R/r$ equals $\mathrm{(A)\ } 1+\sqrt{2} \mathrm{(B) \ }\frac{2+\sqrt{2}}{2} \mathrm{(C) \ } \frac{\sqrt{2}-1}{2} \mathrm{(D) \ } \frac{1+\sqrt{2}}{2} \mathrm{(E) \ }2(2-\sqrt{2})$