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Geometry with angle bisector and perpendicular bisectors

Source: ARO Regional stage 2023 11.8

February 16, 2023
geometryperpendicular bisectorRussia

Problem Statement

Given is a triangle ABCABC with circumcenter OO. Points D,ED, E are chosen on the angle bisector of ∠ABC\angle ABC such that EA=EB,DB=DCEA=EB, DB=DC. If P,QP, Q are the circumcenters of (AOE),(COD)(AOE), (COD), prove that either the line PQPQ coincides with ACAC or PQCAPQCA is cyclic.
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