AMC 12 2011a Problem 17

Circles with radii $1$, $2$, and $3$ are mutually externally tangent. What is the area of the triangle determined by the points of tangency?

\textbf{(A)}\ \frac{3}{5} \textbf{(B)}\ \frac{4}{5} \textbf{(C)}\ 1 \textbf{(D)}\ \frac{6}{5} \textbf{(E)}\ \frac{4}{3}