{"status": "success", "data": {"description_md": "A circle with center $O$ has radius 25. Chord $\\overline{AB}$ of length 30 and chord $\\overline{CD}$ of length 14 intersect at point $P$. The distance between the midpoints of the two chords is 12. The quantity $OP^2$ can be represented as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find the remainder where $m+n$ is divided by 1000.\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>A circle with center <span class=\"katex--inline\">O</span> has radius 25. Chord <span class=\"katex--inline\">\\overline{AB}</span> of length 30 and chord <span class=\"katex--inline\">\\overline{CD}</span> of length 14 intersect at point <span class=\"katex--inline\">P</span>. The distance between the midpoints of the two chords is 12. The quantity <span class=\"katex--inline\">OP^2</span> can be represented as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find the remainder where <span class=\"katex--inline\">m+n</span> is divided by 1000.</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": 5, "problem_name": "2011 AIME II Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/11_aime_II_p11", "prev": "/problem/11_aime_II_p09"}}