2000 Pascal Problem 25

\triangle ABC is an isosceles triangle in which AB = AC = 10 and BC = 12. The points S and R are on BC such that BS : SR : RC = 1{:}2{:}1. The midpoints of AB and AC are P and Q respectively. Perpendiculars are drawn from P and R to SQ meeting at M and N respectively. The length of MN is

\textbf{(A)}\ \frac{9}{\sqrt{13}}\quad \textbf{(B)}\ \frac{10}{\sqrt{13}}\quad \textbf{(C)}\ \frac{11}{\sqrt{13}}\quad \textbf{(D)}\ \frac{12}{\sqrt{13}}\quad \textbf{(E)}\ \frac{5}{2}

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.