IR-MO 2003 Problem 25

Let $A,B,C,Q$ be fixed points on plane. $M,N,P$ are intersection points of $AQ,BQ,CQ$ with $BC,CA,AB$ . $D',E',F'$ are tangency points of incircle of $ABC$ with $BC,CA,AB$ . Tangents drawn from $M,N,P$ (not triangle sides) to incircle of $ABC$ make triangle $DEF$ . Prove that $DD',EE',FF'$ intersect at $Q$ .