Question 56
The circle with the center $O$ is tangent to the sides $[AB]$, $[BC]$, $[CD]$ and $[DA]$ of the convex quadrilateral $ABCD$ at the points $M$, $N$, $K$ and $L$ respectively. The straight lines $MN$ and $AC$ are parallel and the straight line $MK$ intersects the line $LN$ at the point $P$. Prove that the points $A$, $M$, $P$, $O$ and $L$ are concyclic.