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On concyclicity (Indonesia Stage 1 TST for IMO 2022)

Source: Indonesian Stage 1 TST for IMO 2022, Test 3 (Geometry)

December 25, 2021
geometrydiametercircumcircleConcyclic

Problem Statement

Let ABAB be the diameter of circle Γ\Gamma centred at OO. Point CC lies on ray AB→\overrightarrow{AB}. The line through CC cuts circle Γ\Gamma at DD and EE, with point DD being closer to CC than EE is. OFOF is the diameter of the circumcircle of triangle BODBOD. Next, construct CFCF, cutting the circumcircle of triangle BODBOD at GG. Prove that O,A,E,GO,A,E,G are concyclic.
(Possibly proposed by Pak Wono)
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