MathDB

10.7

Part of 2024 Sharygin Geometry Olympiad

Problems(1)

Chevian circle of I, projections

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

8/7/2024
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.
geogeometry