Question 13
Let $ABC$ be a triangle and let $\gamma = \angle ACB$ be such that $\gamma / 2 \lt \angle BAC$ and $\gamma / 2 \lt \angle CBA$. Let $D$ be the point on the segment $BC$ such that $\angle BAD = \gamma / 2$. Let $E$ be the point on the segment $CA$ such that $\angle EBA = \gamma / 2$. Furthermore, let $F$ be the intersection point of the bisector of $\angle ACB$ and the segment $AB$. Show that $EF + FD = AB$.