Let ABC be a triangle, and let the angle bisectors of its angles CAB and ABC meet the sides BC and CA at the points D and F, respectively. The lines AD and BF meet the line through the point C parallel to AB at the points E and G respectively, and we have FG \equal{} DE. Prove that CA \equal{} CB.
Original formulation:
Let ABC be a triangle and L the line through C parallel to the side AB. Let the internal bisector of the angle at A meet the side BC at D and the line L at E and let the internal bisector of the angle at B meet the side AC at F and the line L at G. If GF \equal{} DE, prove that AC \equal{} BC. geometryincentertrigonometryangle bisectorIMO Shortlist