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Collinearity of points on angle bisectors

Source: Moldova TST Problem 2

March 31, 2015
geometryincenterangle bisector

Problem Statement

Consider a triangle △ABC\triangle ABC, let the incircle centered at II touch the sides BC,CA,ABBC,CA,AB at points D,E,FD,E,F respectively. Let the angle bisector of ∠BIC\angle BIC meet BCBC at MM, and the angle bisector of ∠EDF\angle EDF meet EFEF at NN. Prove that A,M,NA,M,N are collinear.
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