{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ have side lengths $AB=30$, $BC=32$, and $AC=34$. Point $X$ lies in the interior of $\\overline{BC}$, and points $I_1$ and $I_2$ are the incenters of $\\triangle ABX$ and $\\triangle ACX$, respectively. Find the minimum possible area of $\\triangle AI_1I_2$ as $X$ varies along $\\overline{BC}$.\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>Let <span class=\"katex--inline\">\\triangle ABC</span> have side lengths <span class=\"katex--inline\">AB=30</span>, <span class=\"katex--inline\">BC=32</span>, and <span class=\"katex--inline\">AC=34</span>. Point <span class=\"katex--inline\">X</span> lies in the interior of <span class=\"katex--inline\">\\overline{BC}</span>, and points <span class=\"katex--inline\">I_1</span> and <span class=\"katex--inline\">I_2</span> are the incenters of <span class=\"katex--inline\">\\triangle ABX</span> and <span class=\"katex--inline\">\\triangle ACX</span>, respectively. Find the minimum possible area of <span class=\"katex--inline\">\\triangle AI_1I_2</span> as <span class=\"katex--inline\">X</span> varies along <span class=\"katex--inline\">\\overline{BC}</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2018 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/18_aime_I_p14", "prev": "/problem/18_aime_I_p12"}}