MathNet 2016-part-04 — 184 problems (EN–VI) Question 44

Let $ABC$ be a right triangle with legs $AB$ and $AC$. The bisector of the angle $ACB$ intersects $AB$ in $D$ and the perpendicular in $B$ on $BC$ in $E$. Denote $F$ the reflection of $E$ across $B$ and $P$ the intersection of the lines $DF$ and $BC$. Prove that $EP \perp CF$.
Cătălin Cristea