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IMO ShortList 1999, geometry problem 1

Source: IMO ShortList 1999, geometry problem 1

November 13, 2004
geometrycircumcircleperimetergeometric inequalityTriangleIMO Shortlist

Problem Statement

Let ABC be a triangle and MM be an interior point. Prove that
min⁡{MA,MB,MC}+MA+MB+MC<AB+AC+BC. \min\{MA,MB,MC\}+MA+MB+MC<AB+AC+BC.
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