Question 83
Let $\omega$ be the circumcircle of an acute triangle $ABC$. Let $D$ be the midpoint of arc $\overset{\frown}{BAC}$ in $\omega$ and $I$ be the incenter of triangle $ABC$. Suppose $DI$ intersects $BC$ at $E$ and $\omega$ at $F$ for the second time. Suppose the parallel line to $AI$ from $E$ meets $AF$ at $P$. Prove that $PE$ is the bisector of $\angle BPC$.