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Proving inequality geometry problem

Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P5 day 2

November 11, 2024
geometryinequalitiescircumcircle

Problem Statement

In triangle ABCABC, DD is the middle point of side BCBC and MM is a point on segment ADAD such that AM=3MDAM=3MD. The barycenter of ABCABC and MM are on the inscribed circumference of ABCABC. Prove that AB+AC>3BCAB+AC>3BC.
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