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4

Part of 2005 Tuymaada Olympiad

Problems(1)

Nagel cevians are sides of triangle

Source: Tuymaada Mathematical Olympiad 2005, Day 1, Problem 4

7/30/2005
In a triangle ABCABC, let A1A_{1}, B1B_{1}, C1C_{1} be the points where the excircles touch the sides BCBC, CACA and ABAB respectively. Prove that AA1A A_{1}, BB1B B_{1} and CC1C C_{1} are the sidelenghts of a triangle.
Proposed by L. Emelyanov
inequalitiesgeometrytrigonometry3D geometrytetrahedrontriangle inequalitygeometry unsolved