2017 AMC 10A Problem 17

Distinct points P, Q, R, S lie on the circle x^2+y^2=25 and have integer coordinates. The distances PQ and RS are irrational numbers. What is the greatest possible value of the ratio \frac{PQ}{RS}?

\textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 3\sqrt{5}\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 5\sqrt{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.