BALTIC-WAY 1993 Problem 18

In the triangle $ABC$ , $|AB|=15,|BC|=12,|AC|=13$ . Let the median $AM$ and bisector $BK$ intersect at point $O$ , where $M\in BC,K\in AC$ . Let $OL\perp AB,L\in AB$ . Prove that $\angle OLK=\angle OLM$ .