2011 Pascal Problem 19

Two circles are centred at the origin, as shown. The point P(8,6) is on the larger circle and the point S(0,k) is on the smaller circle. If QR = 3, what is the value of k?

\textbf{(A)}\ 3.5\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 6.5\quad \textbf{(E)}\ 7

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.