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A, P, Q, E are concylcic; isogonal conjugate

Source: 9.8 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 6, 2024
geogeometry

Problem Statement

Let points PP and QQ be isogonally conjugated with respect to a triangle ABCABC. The line PQPQ meets the circumcircle of ABCABC at point XX. The reflection of BCBC about PQPQ meets AXAX at point EE. Prove that A,P,Q,EA, P, Q, E are concyclic.
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