AHSME 1979 Problem 16

A circle with area $A_1$ is contained in the interior of a larger circle with area $A_1+A_2$. If the radius of the larger circle is $3$, and if $A_1 , A_2, A_1 + A_2$ is an arithmetic progression, then the radius of the smaller circle is $\textbf{(A) }\frac{\sqrt{3}}{2} \textbf{(B) }1 \textbf{(C) }\frac{2}{\sqrt{3}} \textbf{(D) }\frac{3}{2} \textbf{(E) }\sqrt{3}$