Let ABC be an acute triangle with altitude AH, and let P be a variable point such that the angle bisectors k and ℓ of ∠PBC and ∠PCB, respectively, meet on AH. Let k meet AC at E, ℓ meet AB at F, and EF meet AH at Q. Prove that as P varies, line PQ passes through a fixed point. conicshyperbolageometryprojective geometry