IMO 1989 LL MON70

Three mutually nonparallel lines li (i = 1, 2, 3) are given

IMO 1989 LL MON70

Origin: MON

Problem

Three mutually nonparallel lines li (i = 1, 2, 3) are given in a plane. The lines li determine a triangle and reflections fi with axes on lines li. Prove that for every point of the plane, there exists a finite composition of the reflections fi that maps that point to a point interior to the triangle.