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OI passes through isogonal of I wrt triangle A'B'C', angle bisectors

Source: 2006 VMEO III Shortlist SL G4 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__viet

October 29, 2021
geometryisogonalIsogonal conjugateangle bisector

Problem Statement

Let ABCABC be a triangle with circumscribed and inscribed circles (O)(O) and (I)(I) respectively. AA′AA',BB′BB',CC′CC' are the bisectors of triangle ABCABC. Prove that OIOI passes through the the isogonal conjugate of point II with respect to triangle A′B′C′A'B'C'.
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