1979 AHSME 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}\qquad \textbf{(B) }1\qquad \textbf{(C) }\frac{2}{\sqrt{3}}\qquad \textbf{(D) }\frac{3}{2}\qquad \textbf{(E) }\sqrt{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.