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2017 AMC 10A #17

Source: 2017 AMC 10A #17

February 8, 2017
AMCAMC 10AMC 10 A2017 AMC 10Ageometry

Problem Statement

Distinct points PP, QQ, RR, SS lie on the circle x2+y2=25x^2+y^2=25 and have integer coordinates. The distances PQPQ and RSRS are irrational numbers. What is the greatest possible value of the ratio PQRS\frac{PQ}{RS }?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 35<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> 52<span class='latex-bold'>(A)</span>\ 3\qquad<span class='latex-bold'>(B)</span>\ 5\qquad<span class='latex-bold'>(C)</span>\ 3\sqrt{5}\qquad<span class='latex-bold'>(D)</span>\ 7\qquad<span class='latex-bold'>(E)</span>\ 5\sqrt{2}
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