{"status": "success", "data": {"description_md": "The perimeter of triangle $APM$ is $152,$ and the angle $PAM$ is a right angle. A circle of radius $19$ with center $O$ on $\\overline{AP}$ is drawn so that it is tangent to $\\overline{AM}$ and $\\overline{PM}.$ Given that $OP=m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The perimeter of triangle <span class=\"katex--inline\">APM</span> is <span class=\"katex--inline\">152,</span> and the angle <span class=\"katex--inline\">PAM</span> is a right angle. A circle of radius <span class=\"katex--inline\">19</span> with center <span class=\"katex--inline\">O</span> on <span class=\"katex--inline\">\\overline{AP}</span> is drawn so that it is tangent to <span class=\"katex--inline\">\\overline{AM}</span> and <span class=\"katex--inline\">\\overline{PM}.</span> Given that <span class=\"katex--inline\">OP=m/n,</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers, find <span class=\"katex--inline\">m+n.</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 6, "problem_name": "2002 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_II_p15", "prev": "/problem/02_aime_II_p13"}}