2009 AMC 12A Problem 16

A circle with center C is tangent to the positive x and y-axes and externally tangent to the circle centered at (3,0) with radius 1. What is the sum of all possible radii of the circle with center C?

\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 9

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