AMC 12 2009a 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 \textbf{(B)}\ 4 \textbf{(C)}\ 6 \textbf{(D)}\ 8 \textbf{(E)}\ 9