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2001 Spanish Mathematical Olympiad, Problem 3

Source: Spanish Mathematical Olympiad 2001

June 6, 2017
triangle inequalitygeometry

Problem Statement

You have five segments of lengths a1,a2,a3,a4,a_1, a_2, a_3, a_4, and a5a_5 such that it is possible to form a triangle with any three of them. Demonstrate that at least one of those triangles has angles that are all acute.
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