IMO 2016 Shortlist G4

Let ABC be a triangle with AB = AC 6= BC and let I be its incentre. The line BI meets AC at D, and the line through D pe...

IMO 2016 Shortlist G4

Category: Geometry

Problem

Let ABC be a triangle with AB = AC 6= BC and let I be its incentre. The line BI meets AC at D, and the line through D perpendicular to AC meets AI at E. Prove that the reflection of I in AC lies on the circumcircle of triangle BDE.