ISL 1989 Problem 63

Let $l_i,$ $i = 1,2,3$ be three non-collinear straight lines in the plane, which build a triangle, and $f_i$ the axial reflections in $l_i$ . Prove that for each point $P$ in the plane there exists finite interconnections (compositions) of the reflections of $f_i$ which carries $P$ into the triangle built by the straight lines $l_i,$ i.e. maps that point to a point interior to the triangle.