{"status": "success", "data": {"description_md": "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 $\\frac{PQ}{RS}$?\n\n$\\textbf{(A)}\\ 3\\qquad\\textbf{(B)}\\ 5\\qquad\\textbf{(C)}\\ 3\\sqrt{5}\\qquad\\textbf{(D)}\\ 7\\qquad\\textbf{(E)}\\ 5\\sqrt{2}$", "description_html": "<p>Distinct points  <span class=\"katex--inline\">P</span> ,  <span class=\"katex--inline\">Q</span> ,  <span class=\"katex--inline\">R</span> ,  <span class=\"katex--inline\">S</span>  lie on the circle  <span class=\"katex--inline\">x^2+y^2=25</span>  and have integer coordinates. The distances  <span class=\"katex--inline\">PQ</span>  and  <span class=\"katex--inline\">RS</span>   are irrational numbers. What is the greatest possible value of the ratio  <span class=\"katex--inline\">\\frac{PQ}{RS}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3\\qquad\\textbf{(B)}\\ 5\\qquad\\textbf{(C)}\\ 3\\sqrt{5}\\qquad\\textbf{(D)}\\ 7\\qquad\\textbf{(E)}\\ 5\\sqrt{2}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2017 AMC 10A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10A_p18", "prev": "/problem/17_amc10A_p16"}}