Let ABC be a triangle.
r and s are the angle bisectors of ∠ABC and ∠BCA, respectively.
The points E in r and D in s are such that AD∥BE and AE∥CD.
The lines BD and CE cut each other at F.
I is the incenter of ABC.Show that if A,F,I are collinear, then AB=AC. geometryincenterParallel LinesBrazilian Math Olympiad 2016