Question 69
Let $ABC$ be a triangle which satisfies $2 \cdot \angle CBA = 3 \cdot \angle ACB$. The points $D$ and $E$ lie on the side $AC$ such that $BD$ and $BE$ divide the angle $\angle CBA$ into three equal angles and such that $D$ lies between $A$ and $E$. Furthermore, let $F$ be the intersection of $AB$ and the angle bisector of $\angle ACB$. Show that $BE$ and $DF$ are parallel.
