Let △ABC be an acute triangle, and let IB,IC, and O denote its B-excenter, C-excenter, and circumcenter, respectively. Points E and Y are selected on AC such that ∠ABY=∠CBY and BE⊥AC. Similarly, points F and Z are selected on AB such that ∠ACZ=∠BCZ and CF⊥AB.Lines IBF and ICE meet at P. Prove that PO and YZ are perpendicular.Proposed by Evan Chen and Telv Cohl geometry2016 USAMOUSAMOUSA(J)MO