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Chevian circle of I, projections

Source: 10.7 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 7, 2024
geogeometry

Problem Statement

Let ABCABC be a triangle with ∠A=60∘\angle A=60^\circ; ADAD, BEBE, and CFCF be its bisectors; P,QP, Q be the projections of AA to EFEF and BCBC respectively; and RR be the second common point of the circle DEFDEF with ADAD. Prove that P,Q,RP, Q, R are collinear.
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