This problem is the same level as last year's P2 or a bit harder, I feel. No hand diagram because I didn't use any diagram~ (I head solved it) Problem: Let ABC be a triangle with AC>AB , and denote its circumcircle by \Omega 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 \widehat{DF} and \widehat{DE} of the incircle, respectively, such that \angle BXD = \angle DYC. Let line XY meet line BC at K. Let T be the point on \Omega such that KT is tangent to \Omega and T is on the same side of line BC as A. Prove that lines TD and AI meet on \Omega. We begin with the following claim! Points B,X,Y,C-are concyclic Because CD-is tangent to the incircle, we get that \angle CYD=\angle BXD and \angle CDY=\angle DXY. So \angle BXD+\angle DXY+YCB=180 \implies \angle BXY+\angle YCB=180.
Also note that K-B-C is radical axis of the inci...