Isoconjugation with pole the barycentric square of a point

Let ABC be a triangle, P and Q two points, PaPbPc the cevian triangle of P. The line PQ cuts the conic (QBCPbPc) again at Qa. Define Qb, Qc cyclically. Then the lines AQa, BQb and CQc are concurrent at Q*= the image of Q under the isoconjugation with pole P^2 (barycentric square of P).
Angel Montesdeoca. Junio, 2016