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Geo involving centers of (AOH), (BOH), (COH)

Source: Serbia MO 2023 P1

April 2, 2023
geometry

Problem Statement

Given is a triangle ABCABC with circumcenter OO and orthocenter HH. If Oa,Ob,OcO_a, O_b, O_c denote the circumcenters of △AOH\triangle AOH, △BOH\triangle BOH, △COH\triangle COH, then prove that AOa,BOb,COcAO_a, BO_b, CO_c are concurrent.
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