AMC 12 2025a Problem 8

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

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