Let ABC be a triangle and P,P* two isogonal conjugate points. Denote: H1,H2,H3 = the orthocenters of PBC, PCA, PAB, resp. and Ha,Hb,Hc = the orthocenters of P*BC, P*CA, P*AB, resp.
The circumcircles of: (1) H1HbHc, H2HcHa, H3HaHb (2) HaH2H3, HbH3H1, HcH1H2 are concurrent.
Antreas P. Hatzipolakis, 5 July 2013