{"status": "success", "data": {"description_md": "Suppose that the angles of $\\triangle ABC$ satisfy $\\cos(3A) + \\cos(3B) + \\cos(3C) = 1$. Two sides of the triangle have lengths $10$ and $13$. There is a positive integer $m$ so that the maximum possible length for the remaining side of $\\triangle ABC$ is $\\sqrt{m}$. Find $m$.\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>Suppose that the angles of <span class=\"katex--inline\">\\triangle ABC</span> satisfy <span class=\"katex--inline\">\\cos(3A) + \\cos(3B) + \\cos(3C) = 1</span>. Two sides of the triangle have lengths <span class=\"katex--inline\">10</span> and <span class=\"katex--inline\">13</span>. There is a positive integer <span class=\"katex--inline\">m</span> so that the maximum possible length for the remaining side of <span class=\"katex--inline\">\\triangle ABC</span> is <span class=\"katex--inline\">\\sqrt{m}</span>. Find <span class=\"katex--inline\">m</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": 5, "problem_name": "2014 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/14_aime_II_p13", "prev": "/problem/14_aime_II_p11"}}