IT-CESENATICO 1994 Problem 4

Let $ABC$ be a triangle contained in one of the halfplanes determined by a line $r$ . Points $A',B',C'$ are the reflections of $A,B,C$ in $r,$ respectively. Consider the line through $A'$ parallel to $BC$ , the line through $B'$ parallel to $AC$ and the line through $C'$ parallel to $AB$ . Show that these three lines have a common point.