2021 Fall AMC 12B Problem 24

Triangle ABC has side lengths AB = 11, BC=24, and CA = 20. The bisector of \angle{BAC} intersects \overline{BC} in point D, and intersects the circumcircle of \triangle{ABC} in point E \ne A. The circumcircle of \triangle{BED} intersects the line AB in points B and F \ne B. What is CF?

\textbf{(A) } 28 \qquad \textbf{(B) } 20\sqrt{2} \qquad \textbf{(C) } 30 \qquad \textbf{(D) } 32 \qquad \textbf{(E) } 20\sqrt{3}

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