Let ABC be a triangle. Let (O1),(O2), (O3) be the reflections of the circumcircle (O) in the cevians AI, BI, CI, resp.
Let (O11), (O22), (O33) be the reflections of (O1), (O2), (O3) in BC, CA, AB, resp., L1,L2,L3 the radical axes of [(O22),(O33)], [(O33),(O11)], [(O11), (O22)], resp. and M1,M2,M3 the parallels to L1,L2,L3 through A,B,C resp.
The lines M1,M2,M3 are concurrent.
Point of concurrence?
Locus: For P instead of I, such that M1,M2,M3 are concurrent?
APH, 4 December 2011
The locus is McCay cubic, circumcircle, line at infinity and a sextic with no real points.
Francisco Javier García Capitán
5 December 2011