Problem 2.  Let ABC be a triangle with AC > AB , and denote its circumcircle by Ω and incentre by I . Let its incircle meet sides BC, CA, AB at D, E, F respectively. Let X and Y be two points on minor arcs $\stackrel{⏜}{DF}$ and  $\stackrel{⏜}{DE}$ of the incircle, respectively, such that ∠ BXD = ∠ DYC . Let line XY meet line BC at K . Let T be the point on Ω such that KT is tangent to Ω and T is on the same side of line BC as A . Prove that lines TD and AI meet on Ω.