Question 153
Let $ABCD$ be a convex quadrilateral, $F$ a point on the segment $CD$, and $E$ the intersection point of $AC$ with $BF$. It is known that $AB = FC$, $AE = 14$, $BE = 10\sqrt{2}$, $\widehat{BAC} = \widehat{BFD}$, $\widehat{BEA} = 45^\circ$. What is the length of the segment $EF$?