Triangle with the bisectors of the exterior angles. Collinearity.

In any non-isosceles triangle ABC, the bisectors of the exterior angles at A, B, and C meet the opposite sides at points D, E, and F respectively. Prove that D, E, and F are collinear.

See also: Ceva's Theorem, Menelaus' theorem, Blanchet Theorem, Gergonne Point, Nagel Point, Pentagons & Pentagrams.