Question 25
(POL) The bisectors of angles $A,B,C$ of a triangle $ABC$ meet its circumcircle again at the points $K,L,M$, respectively. Let $R$ be an internal point on the side $AB$. The points $P$ and $Q$ are defined by the following conditions: $RP$ is parallel to $AK$, and $BP$ is perpendicular to $BL$; $RQ$ is parallel to $BL$, and $AQ$ is perpendicular to $AK$. Show that the lines $KP,LQ,MR$ have a point in common.