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Circumcentre on perpendicular bisector (BxMO2021 P3)

Source: BxMO2021 problem 3

May 3, 2021
geometryBxMO

Problem Statement

A cyclic quadrilateral ABXCABXC has circumcentre OO. Let DD be a point on line BXBX such that AD=BDAD = BD. Let EE be a point on line CXCX such that AE=CEAE = CE. Prove that the circumcentre of triangle △DEX\triangle DEX lies on the perpendicular bisector of OAOA.
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