2024 Mock AMC 12 - Problem 22

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\sqrt{6}, find the square of the area of BEF.

\textbf{(A) }16+7\sqrt{6}\qquad\textbf{(B) }288\qquad\textbf{(C) }294\qquad\textbf{(D) }600\qquad\textbf{(E) }24-3\sqrt{15}