Problems(1)
Triangle ABC has circumcircle Ω and incircle ω, where ω is tangent to BC,CA,AB at D,E,F, respectively. T is an arbitrary point on ω. EF meets BC at K, AT meets Ω again at P, PK meets Ω again at S. X is a point on Ω such that S,D,X are colinear. Let Y be the intersection of AX and EF, prove that YT is tangent to ω.Proposed by chengbilly geometryIMOC