Question 96
Let $\odot I$ be the incircle of $\triangle ABC$ with $AB \gt AC$. $\odot I$ is tangent to $BC$ and $AD$ at $D$ and $E$, respectively. The tangent line $EP$ of $\odot I$ intersects the extended line of $BC$ at $P$. Segment $CF$ is parallel to $PE$ and intersects $AD$ at point $F$. Line $BF$ intersects $\odot I$ at points $M$ and $N$ such that $M$ is on segment $BF$. Segment $PM$ intersects $\odot I$ at the other point $Q$. Prove that $\angle ENP = \angle ENQ$.