IMO 2016 Shortlist G7
Let I be the incentre of a non-equilateral triangle ABC, IA be the A-excentre, I0 A be the reflection of IA in BC, and l...
Category: Geometry
Problem
Let I be the incentre of a non-equilateral triangle ABC, IA be the A-excentre, I0 A be the reflection of IA in BC, and lA be the reflection of line AI0 A in AI. Define points IB,I0 B and line lB analogously. Let P be the intersection point of lA and lB. (a) Prove that P lies on line OI where O is the circumcentre of triangle ABC. (b) Let one of the tangents from P to the incircle of triangle ABC meet the circumcircle at points X and Y . Show that ∠XIY = 120◦ .