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Show Two Segments Meet on AD

Source: 2011 MMO Problem #4

September 11, 2011
geometryincentertrigonometryangle bisectorgeometry unsolved

Problem Statement

Let DD be the foot of the internal bisector of the angle ∠A\angle A of the triangle ABCABC. The straight line which joins the incenters of the triangles ABDABD and ACDACD cut ABAB and ACAC at MM and NN, respectively. Show that BNBN and CMCM meet on the bisector ADAD.
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