RO-TST 2004 Problem 14

Let $O$ be a point in the plane of the triangle $ABC$ . A circle $\mathcal{C}$ which passes through $O$ intersects the second time the lines $OA,OB,OC$ in $P,Q,R$ respectively. The circle $\mathcal{C}$ also intersects for the second time the circumcircles of the triangles $BOC$ , $COA$ and $AOB$ respectively in $K,L,M$ .

Prove that the lines $PK,QL$ and $RM$ are concurrent.