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2013 ToT Fall Senior O p3, 4 points concyclic, equilateral, circumcircle

Source:

March 22, 2020
geometryEquilateralcircumcircleConcyclic

Problem Statement

Let ABCABC be an equilateral triangle with centre OO. A line through CC meets the circumcircle of triangle AOBAOB at points DD and EE. Prove that points A,OA, O and the midpoints of segments BD,BEBD, BE are concyclic.
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