IMO 2019 Shortlist G7
The incircle ω of acute-angled scalene triangle ABC has centre I and meets sides BC, CA, and AB at D, E, and F, respecti...
Category: Geometry
Problem
The incircle ω of acute-angled scalene triangle ABC has centre I and meets sides BC, CA, and AB at D, E, and F, respectively. The line through D perpendicular to EF meets ω again at R. Line AR meets ω again at P. The circumcircles of triangles PCE and PBF meet again at Q ‰ P. Prove that lines DI and PQ meet on the external bisector of angle BAC. (India)