Question 56
$M$ is the midpoint of the side $AC$ of triangle $ABC$, $L$ is a point on the segment $BC$. The line $LM$ intersects the ray $BA$ in the point $K$. $P$ is the point on the segment $BM$ such that $PM$ is a bisector of angle $LPK$. The line $\ell$ passes through $A$ and is parallel to $BM$. Prove that the projection of the point $M$ onto the line $\ell$ belongs to the line $PK$.
