{"status": "success", "data": {"description_md": "Given an acute triangle $ABC$ with $AB = 7$, construct a point $D$ on the interior of segment $AC$ such that $CD=7$. Then, let points $E$ and $F$ be the midpoints of $AD$ and $BC$, respectively. Given that $EF = 5$ and the area of $ABC$ is $18\\sqrt6$, find the square of the area of $BEF$.\n\n$\\textbf{(A)}~16+7\\sqrt6\\qquad\\textbf{(B)}~288\\qquad\\textbf{(C)}~294\\qquad\\textbf{(D)}~600\\qquad\\textbf{(E)}~24-3\\sqrt{15}$", "description_html": "<p>Given an acute triangle <span class=\"katex--inline\">ABC</span> with <span class=\"katex--inline\">AB = 7</span>, construct a point <span class=\"katex--inline\">D</span> on the interior of segment <span class=\"katex--inline\">AC</span> such that <span class=\"katex--inline\">CD=7</span>. Then, let points <span class=\"katex--inline\">E</span> and <span class=\"katex--inline\">F</span> be the midpoints of <span class=\"katex--inline\">AD</span> and <span class=\"katex--inline\">BC</span>, respectively. Given that <span class=\"katex--inline\">EF = 5</span> and the area of <span class=\"katex--inline\">ABC</span> is <span class=\"katex--inline\">18\\sqrt6</span>, find the square of the area of <span class=\"katex--inline\">BEF</span>.</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~16+7\\sqrt6\\qquad\\textbf{(B)}~288\\qquad\\textbf{(C)}~294\\qquad\\textbf{(D)}~600\\qquad\\textbf{(E)}~24-3\\sqrt{15}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2024 Mock AMC 12 - Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/2024_mock_amc12-p23", "prev": "/problem/2024_mock_amc12-p21"}}