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concurrent wanted, symmetric of projections of vertices on sides wrt centroid

Source: 2015 Saudi Arabia GMO TST II p3

August 1, 2020
geometryconcurrencyconcurrentsymmetryCentroid

Problem Statement

Let ABCABC be a triangle and GG its centroid. Let Ga,GbG_a, G_b and GcG_c be the orthogonal projections of GG on sides BC,CABC, CA, respectively ABAB. If Sa,SbS_a, S_b and ScS_c are the symmetrical points of Ga,GbG_a, G_b, respectively GcG_c with respect to GG, prove that ASa,BSbAS_a, BS_b and CScCS_c are concurrent.
Liana Topan
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