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2 pairs of isogonal conjugated points and coaxial circles

Source: 9.3 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 6, 2024
geogeometry

Problem Statement

Let (P,P′)(P, P') and (Q,Q′)(Q, Q') be two pairs of points isogonally conjugated with respect to a triangle ABCABC, and RR be the common point of lines PQPQ and P′Q′P'Q'. Prove that the pedal circles of points PP, QQ, and RR are coaxial.
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