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MCEB is cyclic iff MB = BG

Source: Mathematics Regional Olympiad of Mexico West 2019 P4

September 9, 2022
Concyclicgeometrycyclic quadrilateral

Problem Statement

Let ABCABC be a triangle. MM the midpoint of ABAB and LL the midpoint of BCBC. We denote by GG the intersection of ALAL with CMCM and we take EE a point such that GG is the midpoint of the segment AEAE. Prove that the quadrilateral MCEBMCEB is cyclic if and only if MB=BGMB = BG.
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