{"status": "success", "data": {"description_md": "Triangle $ABC$ is isosceles, with $AB=AC$ and altitude $AM=11.$ Suppose that there is a point $D$ on $\\overline{AM}$ with $AD=10$ and $\\angle BDC=3\\angle BAC.$ Then the perimeter of $\\triangle ABC$ may be written in the form $a+\\sqrt{b},$ where $a$ and $b$ are integers. Find $a+b.$<br><br>$\\includegraphics[width=117, height=174, totalheight=174]{https://latex.artofproblemsolving.com/4/d/8/4d85729df9c98d898f6aba4cd738ce485316a0ca.png}$\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>Triangle <span class=\"katex--inline\">ABC</span> is isosceles, with <span class=\"katex--inline\">AB=AC</span> and altitude <span class=\"katex--inline\">AM=11.</span> Suppose that there is a point <span class=\"katex--inline\">D</span> on <span class=\"katex--inline\">\\overline{AM}</span> with <span class=\"katex--inline\">AD=10</span> and <span class=\"katex--inline\">\\angle BDC=3\\angle BAC.</span> Then the perimeter of <span class=\"katex--inline\">\\triangle ABC</span> may be written in the form <span class=\"katex--inline\">a+\\sqrt{b},</span> where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are integers. Find <span class=\"katex--inline\">a+b.</span><br/><br/><img src=\"https://latex.artofproblemsolving.com/4/d/8/4d85729df9c98d898f6aba4cd738ce485316a0ca.png\" width=\"117\" height=\"174\" class=\"problem-image\"/></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": 4, "problem_name": "1995 AIME Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/95_aime_p10", "prev": "/problem/95_aime_p08"}}