1999 Fermat Problem 24

Two circles C_1 and C_2 touch each other externally and the line l is a common tangent. The line m is parallel to l and touches the two circles C_1 and C_3. The three circles are mutually tangent. If the radius of C_2 is 9 and the radius of C_3 is 4, what is the radius of C_1?

\textbf{(A)}\ 10.4\quad \textbf{(B)}\ 11\quad \textbf{(C)}\ 8\sqrt{2}\quad \textbf{(D)}\ 12\quad \textbf{(E)}\ 7\sqrt{3}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.