{"status": "success", "data": {"description_md": "Let $ABCD$ be a unit square and $E$ be a point in $ABCD$ such that $\\triangle ABE$ is an equilateral triangle. If $\\frac{\\sqrt m}{n}$ is the ratio of the areas of $ABE$ and $ABCD$, where $m$ and $n$ are positive integers with $m$ not divisible by the square of any prime, compute the value of $m+n$.", "description_html": "<p>Let <span class=\"katex--inline\">ABCD</span> be a unit square and <span class=\"katex--inline\">E</span> be a point in <span class=\"katex--inline\">ABCD</span> such that <span class=\"katex--inline\">\\triangle ABE</span> is an equilateral triangle. If <span class=\"katex--inline\">\\frac{\\sqrt m}{n}</span> is the ratio of the areas of <span class=\"katex--inline\">ABE</span> and <span class=\"katex--inline\">ABCD</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are positive integers with <span class=\"katex--inline\">m</span> not divisible by the square of any prime, compute the value of <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "Christmas Contest - Guts Round - Set 1 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}