Oab, Oac = the circumcenters of AA'B, AA'C, resp.
(O1) = the circumcircle of A'OabOac. Similarly (O2), (O3).
P* = the radical center of (O1),(O2), (O3)
For P = G, the G* is lyimg on the Euler line of ABC.
Locus: Which is the locus of P such that P* is lying 1. on the OP line 2. on the Euler Line of ABC?
Antreas P. Hatzipolakis, 1 September 2014