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triangle inscribed in triangle, 1 of 2 smallest sides is the inner's triangle

Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p6

April 17, 2020
geometrygeometric inequalityinscribed triangleinscribedside

Problem Statement

One triangle lies inside another. Prove that at least one of the two smallest sides (out of six) is the side of the inner triangle.