2025 AMC 12A Problem 8

Pentagon ABCDE is inscribed in a circle, and \angle BEC = \angle CED = 30^\circ. Let AC and BD intersect at point F, and suppose that AB = 9 and AD = 24. What is BF?

\textbf{(A)} \dfrac{57}{11} \qquad \textbf{(B)} \dfrac{59}{11} \qquad \textbf{(C)} \dfrac{60}{11} \qquad \textbf{(D)} \dfrac{61}{11} \qquad \textbf{(E)} \dfrac{63}{11}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.