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AB x CC' = AC xBB' if AC'GB' is cyclic

Source: 2013 Saudi Arabia Pre-TST 1.4

September 13, 2020
geometrycyclic quadrilateralCentroid

Problem Statement

ABCABC is a triangle, GG its centroid and A′,B′,C′A',B',C' the midpoints of its sides BC,CA,ABBC,CA,AB, respectively. Prove that if the quadrilateral AC′GB′AC'GB' is cyclic then AB⋅CC′=AC⋅BB′AB \cdot CC' = AC \cdot BB':
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