Question 169
The three points $A$, $B$, $C$ form a triangle. $AB = 4$, $BC = 5$, $AC = 6$. Let the angle bisector of $\angle A$ intersect side $BC$ at $D$. Let the foot of the perpendicular from $B$ to the angle bisector of $\angle A$ be $E$. Let the line through $E$ parallel to $AC$ meet $BC$ at $F$. Compute $DF$.