UA-UMO 1998 Problem 112

The altitude $CD$ of triangle $ABC$ meets the bisector $BK$ of this triangle at $M$ and the altitude $KL$ of $\triangle BKC$ at $N$ . The circumcircle of triangle $BKN$ meets the side $AB$ at point $P\ne B$ . Prove that the triangle $KPM$ is isosceles.