{"status": "success", "data": {"description_md": "Square $ABCD$ has sides of length 1. Points $E$ and $F$ are on $\\overline{BC}$ and $\\overline{CD}$, respectively, so that $\\triangle AEF$ is equilateral. A square with vertex $B$ has sides that are parallel to those of $ABCD$ and a vertex on $\\overline{AE}$. The length of a side of this smaller square is $\\displaystyle \\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b+c$.\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>Square <span class=\"katex--inline\">ABCD</span> has sides of length 1. Points <span class=\"katex--inline\">E</span> and <span class=\"katex--inline\">F</span> are on <span class=\"katex--inline\">\\overline{BC}</span> and <span class=\"katex--inline\">\\overline{CD}</span>, respectively, so that <span class=\"katex--inline\">\\triangle AEF</span> is equilateral. A square with vertex <span class=\"katex--inline\">B</span> has sides that are parallel to those of <span class=\"katex--inline\">ABCD</span> and a vertex on <span class=\"katex--inline\">\\overline{AE}</span>. The length of a side of this smaller square is <span class=\"katex--inline\">\\displaystyle \\frac{a-\\sqrt{b}}{c}</span>, where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are positive integers and <span class=\"katex--inline\">b</span> is not divisible by the square of any prime. Find <span class=\"katex--inline\">a+b+c</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": 4, "problem_name": "2006 AIME II Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/06_aime_II_p07", "prev": "/problem/06_aime_II_p05"}}