{"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 (\\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}).</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": "2018 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/18_aime_I_p14", "prev": "/problem/18_aime_I_p12"}}