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A²+b² > 5c²

Source: Germany Bundeswettbewerb Mathematik 2006, Day 1, Problem 3

April 4, 2006

Problem Statement

Let a,b,ca,b,c be the sidelengths of a triangle such that a2+b2>5c2a^2+b^2 > 5c^2 holds. Prove that cc is the shortest side of the triangle.
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