1871. Collinear Points

 Let I=X(1)- Incenter of ABC. P be a point on Circumcircle of ABC with first barycentric (a^2(x-y)(x-z):...:...)  Pa,Pb,Pc inverse of P in the circles BIC, CIA, AIB resp.

* I, Pa, Pb, Pc lie on same line. 
** Trilinear pole of  line has first barycentric (a (x-y)(x-z):...:...).
Some pairs (P,Q)=(Xi, Xj) where Q is trilinear pole of the line.
{(74, 2349), (98,1821), (99, 799), (100,190)....}