Given a triangle ABC. Let D, E, F, D1, E1, and F1 be the points of tangency of the incircle and excircle corresponding to AC, as shown in the figure. FG and F1G1 are perpendicular to DE and D1E1, respectively (G on DE and G1 on D1E1). Prove that AGCG1 and FGF1G1 are parallelograms.
See also: isolines of problem 1267.