Question 149
Given $\triangle ABC$, $D$ is on $BC$ and $P$ is on $AD$. A line $\ell$ passing through $D$ intersects $AB$, $PB$ at $M$, $E$ respectively, and intersects $AC$ extended and $PC$ extended at $F$, $N$ respectively. Let $DE = DF$. Prove that $DM = DN$.