Let $ABC$ be an acute scalene triangle with altitudes $AE$ $(E \in BC)$ and $BD$ $(D \in AC)$. Point $M$ lies on $AC$, such that $AM = AE$ and $C,A$ and $M$ lie in this order. Point $L$ lies on $BC$, such that $BL=BD$ and $C,B$ and $L$ lie in this order. Let $P$ be the midpoint of $DE$. Prove that $EM,DL$ and the perpendicular from $P$ to $AB$ are concurrent.