2019 IMO Problems/Problem 6

Revision as of 23:27, 26 May 2020 by Ultraman (talk | contribs) (Created page with "==Problem== Let I be the incentre of acute triangle ABC with AB ̸= AC. The incircle ω of ABC is tangent to sides BC, CA, and AB at D, E, and F, respectively. The line throug...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let I be the incentre of acute triangle ABC with AB ̸= AC. The incircle ω of ABC is tangent to 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. Prove that lines DI and PQ meet on the line through A perpendicular to AI.