Question 81
A quadrilateral $ABCD$ is inscribed in a circle, with $AB = 7$ and $BC = 18$. The bisector of $\angle CDA$ intersects side $BC$ at point $E$, and a point $F$ on segment $DE$ satisfies $\angle AED = \angle FCD$. When $BE = 5$ and $EF = 3$, find the length of segment $DF$.