2008 Pascal Problem 25

In the diagram, \triangle PQR is right-angled at P and has PQ = 2 and PR = 2\sqrt{3}. Altitude PL intersects median RM at F. What is the length of PF?

\textbf{(A)}\ \frac{\sqrt{3}}{2}\quad \textbf{(B)}\ \frac{3\sqrt{3}}{7}\quad \textbf{(C)}\ \frac{4\sqrt{3}}{7}\quad \textbf{(D)}\ \frac{5\sqrt{3}}{9}\quad \textbf{(E)}\ \frac{3\sqrt{3}}{5}

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.