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G,B,C,A' concyclic iff GA ⊥ GC (AC=CA')

Source: JBMO Shortlist 2003

October 12, 2017
JBMOgeometry

Problem Statement

Let GG be the centroid of triangle ABCABC, and A′A' the symmetric of AA wrt CC. Show that G,B,C,A′G, B, C, A' are concyclic if and only if GA⊥GCGA \perp GC.
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