AMC 12 2011a Problem 15

The circular base of a hemisphere of radius $2$ rests on the base of a square pyramid of height $6$. The hemisphere is tangent to the other four faces of the pyramid. What is the edge-length of the base of the pyramid?

\textbf{(A)}\ 3\sqrt{2} \textbf{(B)}\ \frac{13}{3} \textbf{(C)}\ 4\sqrt{2} \textbf{(D)}\ 6 \textbf{(E)}\ \frac{13}{2}