Collinear Points, Reflection Points, Circum-Hyperbola

Take any point P not on the circumcircle or orthocenter. Reflect P in the sides producing Pa, Pb, and Pc. Circles PaPbC, PaPcB, and PbPcA intersect at point T on the circumcircle. P and r(P) lie on a rectangular circumhyperbola. This hyperbola intersects the circumcircle at a fourth point Q. P, T, and Q are collinear.