Question 24·Hard·Circles

In the figure, $PQ$ is the diameter of a circle. Point $R$ lies on the circle, and segment $RS$ is perpendicular to $PQ$ at point $S$.

If $PQ=130$ and $PR=13\sqrt{5}$, which choice is the value of $\frac{PQ}{PS}$?

Note: Figure not drawn to scale.