IMO 2020 Shortlist G6

Problem

Let I and IA be the incenter and the A-excenter of an acute-angled triangle ABC with AB ă AC. Let the incircle meet BC at D. The line AD meets BIA and CIA at E and F, respectively. Prove that the circumcircles of triangles AID and IAEF are tangent to each other. (Slovakia)Shortlisted problems 9

imo
mathematics
olympiad
shortlist
geometry