RIOPLATENSE 2000 Problem 5

Let $ABC$ be a triangle with $AB < AC$ , let $L$ be midpoint of arc $BC$ (the point $A$ is not in this arc) of the circumcircle $w$ ( $ABC$ ). Let $E$ be a point in $AC$ where $AE = \frac{AB + AC}{2}$ , the line $EL$ intersects $w$ in $P$ . If $M$ and $N$ are the midpoints of $AB$ and $BC$ , respectively, prove that $AL, BP$ and $MN$ are concurrents