2011 Fermat Problem 19

In the diagram, the two circles are centred at O. Point S is on the larger circle. Point Q is the point of intersection of OS and the smaller circle. Line segment PR is a chord of the larger circle and touches (that is, is tangent to) the smaller circle at Q. Note that OS is the perpendicular bisector of PR. If PR = 12 and QS = 4, then the radius of the larger circle is

\textbf{(A)}\ 6.0\quad \textbf{(B)}\ 5.0\quad \textbf{(C)}\ 6.5\quad \textbf{(D)}\ 7.2\quad \textbf{(E)}\ 20.0

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 Fermat contests here.