{"status": "success", "data": {"description_md": "In a certain circle, the chord of a $d$-degree arc is 22 centimeters long, and the chord of a $2d$-degree arc is 20 centimeters longer than the chord of a $3d$-degree arc, where $d<120.$ The length of the chord of a $3d$-degree arc is $-m+\\sqrt{n}$ centimeters, where $m$ and $n$ are 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>In a certain circle, the chord of a <span class=\"katex--inline\">d</span>-degree arc is 22 centimeters long, and the chord of a <span class=\"katex--inline\">2d</span>-degree arc is 20 centimeters longer than the chord of a <span class=\"katex--inline\">3d</span>-degree arc, where <span class=\"katex--inline\">d&lt;120.</span> The length of the chord of a <span class=\"katex--inline\">3d</span>-degree arc is <span class=\"katex--inline\">-m+\\sqrt{n}</span> centimeters, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are 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": "2001 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/01_aime_I_p14", "prev": "/problem/01_aime_I_p12"}}