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Centroid homothety!

Source: Romania TST 2014 Day 2 Problem 1

January 21, 2015
geometrygeometric transformationhomothetygeometry unsolved

Problem Statement

Let ABCABC be a triangle and let XX,YY,ZZ be interior points on the sides BCBC, CACA, ABAB, respectively. Show that the magnified image of the triangle XYZXYZ under a homothety of factor 44 from its centroid covers at least one of the vertices AA, BB, CC.
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