BALKAN 1991 Problem 1

Let $ABC$ be an acute triangle inscribed in a circle centered at $O$ . Let $M$ be a point on the small arc $AB$ of the triangle's circumcircle. The perpendicular dropped from $M$ on the ray $OA$ intersects the sides $AB$ and $AC$ at the points $K$ and $L$ , respectively. Similarly, the perpendicular dropped from $M$ on the ray $OB$ intersects the sides $AB$ and $BC$ at $N$ and $P$ , respectively. Assume that $KL=MN$ . Find the size of the angle $\angle{MLP}$ in terms of the angles of the triangle $ABC$ .