Reflections of the Circumcircle in the cevians of the Incenter

Let ABC be a triangle. Let (O1),(O2), (O3) be the reflections of the circumcircle (O) in the cevians AI, BI, CI, resp

Let L1 be the common chord (radical axis) of (O2) and (O3) and similarly L2 and L3 (concurrent at I). Let M1, M2, M3 be the parallels to L1,L2,L3 through A,B,C, resp. The lines M1,M2,M3 are concurent.

Point of concurrence?

Generalization:
P instead of I. Locus of P such that M1,M2,M3 are concurrent?

APH, 2 December 2011

The locus of P is: Line at Infinity + Circumcircle + McCay cubic.

Francisco Javier García Capitán
2 December 2011