{"status": "success", "data": {"description_md": "For positive real numbers $s$, let $\\tau(s)$ denote the set of all obtuse triangles that have area $s$ and two sides with lengths $4$ and $10$. The set of all $s$ for which $\\tau(s)$ is nonempty, but all triangles in $\\tau(s)$ are congruent, is an interval $[a,b)$. Find $a^2+b^2$.\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>For positive real numbers <span class=\"katex--inline\">s</span>, let <span class=\"katex--inline\">\\tau(s)</span> denote the set of all obtuse triangles that have area <span class=\"katex--inline\">s</span> and two sides with lengths <span class=\"katex--inline\">4</span> and <span class=\"katex--inline\">10</span>. The set of all <span class=\"katex--inline\">s</span> for which <span class=\"katex--inline\">\\tau(s)</span> is nonempty, but all triangles in <span class=\"katex--inline\">\\tau(s)</span> are congruent, is an interval <span class=\"katex--inline\">[a,b)</span>. Find <span class=\"katex--inline\">a^2+b^2</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": 3, "problem_name": "2021 AIME II Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_II_p06", "prev": "/problem/21_aime_II_p04"}}