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Triangle with sides AB+CD,... is acute

Source: 9.2 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 6, 2024
geogeometry

Problem Statement

Points A,B,C,DA, B, C, D on the plane do not form a rectangle. Let the sidelengths of triangle TT equal AB+CDAB+CD, AC+BDAC+BD, AD+BCAD+BC. Prove that the triangle TT is acute-angled.
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