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Triangles have the same perimeter iff ABC is equilateral

Source: Austrian Mathematical Olympiad 2002, Part 2, D2, P3

June 25, 2011
geometryperimetertrigonometryfunctiongeometry unsolved

Problem Statement

Let HH be the orthocenter of an acute-angled triangle ABCABC. Show that the triangles ABH,BCHABH,BCH and CAHCAH have the same perimeter if and only if the triangle ABCABC is equilateral.
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