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Set of triangles

Source: Indonesia Mathematics Olympiad 2006 Day 1 Problem 3

June 2, 2008
trigonometrygeometry proposedgeometry

Problem Statement

Let S S be the set of all triangles ABC ABC which have property: tan⁡A,tan⁡B,tan⁡C \tan A,\tan B,\tan C are positive integers. Prove that all triangles in S S are similar.
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