2015 Cayley Problem 18

In the diagram, rectangle PQRS has side PQ on the diameter of the semicircle with R and S on the semicircle. If the diameter of the semicircle is 20 and the length of PQ is 16, then the length of PS is

\textbf{(A)}\ 6\quad \textbf{(B)}\ 7\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 9\quad \textbf{(E)}\ 10

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 Cayley contests here.