AHSME 1969 Problem 13

A circle with radius $r$ is contained within the region bounded by a circle with radius $R$. The area bounded by the larger circle is $\frac{a}{b}$ times the area of the region outside the smaller circle and inside the larger circle. Then $R:r$ equals: $\text{(A) }\sqrt{a}:\sqrt{b} \text{(B) } \sqrt{a}:\sqrt{a-b} \text{(C) } \sqrt{b}:\sqrt{a-b} \text{(D) } a:\sqrt{a-b} \text{(E) } b:\sqrt{a-b}$