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Bundeswettbewerb Mathematik 1981 Problem 1.2

Source: Bundeswettbewerb Mathematik 1981 Round 1

September 22, 2022
geometryClassicCentroidparallel

Problem Statement

Prove that if the sides a,b,ca, b, c of a non-equilateral triangle satisfy a+b=2ca + b = 2c, then the line passing through the incenter and centroid is parallel to one of the sides of the triangle.
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