Triangle △ABC is inscribed in circle Ω. Let I denote its incenter and IA its A-excenter. Let N denote the midpoint of arc BAC. Line NIA meets Ω a second time at T. The perpendicular to AI at I meets sides AC and AB at E and F respectively. The circumcircle of △BFT meets BIA a second time at P, and the circumcircle of △CET meets CIA a second time at Q. Prove that PQ passes through the antipodal to A on Ω. geometryconfigurationscircumcircleincenter