{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ be a triangle with $AB = 5, AC = 4, BC = 3.$ Let points $D, E$ be outside of $\\triangle ABC$ such that $\\triangle ABD$ and $\\triangle ACE,$ are equilateral.  The square of the length of $DE$ can be expressed as $p + q\\sqrt r,$ where $p, q, r \\in \\mathbb{N}$, and $r$ is not divisible by the square of any prime. Compute the value of $p + q + r$.", "description_html": "<p>Let <span class=\"katex--inline\">\\triangle ABC</span> be a triangle with <span class=\"katex--inline\">AB = 5, AC = 4, BC = 3.</span> Let points <span class=\"katex--inline\">D, E</span> be outside of <span class=\"katex--inline\">\\triangle ABC</span> such that <span class=\"katex--inline\">\\triangle ABD</span> and <span class=\"katex--inline\">\\triangle ACE,</span> are equilateral.  The square of the length of <span class=\"katex--inline\">DE</span> can be expressed as <span class=\"katex--inline\">p + q\\sqrt r,</span> where <span class=\"katex--inline\">p, q, r \\in \\mathbb{N}</span>, and <span class=\"katex--inline\">r</span> is not divisible by the square of any prime. Compute the value of <span class=\"katex--inline\">p + q + r</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Christmas Contest - Guts Round - Set 5 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}