Problems(1)
Triangle ABC satisfying AB<AC has circumcircle Ω. E,F lies on AC,AB, respectively, such that BCEF is cyclic. T lies on EF such that ⊙(TEF) is tangent to BC at T. A′ is the antipode of A on Ω. TA′,TA intersects Ω again at X,Y, respectively, and EF intersects ⊙(TXY) again at W. Prove that ∡WBA=∡ACWProposed by BlessingOfHeaven geometryIMOC