2006 Pascal Problem 22

In the diagram, each of the three identical circles touch the other two. The circumference of each circle is 36. What is the perimeter of the shaded region?

\textbf{(A)}\ 18\quad \textbf{(B)}\ 6\quad \textbf{(C)}\ 36\quad \textbf{(D)}\ 12\quad \textbf{(E)}\ 24

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 Pascal contests here.