Ab = (IBC) /\ ((I,IB)-B)
ie the other than B intersection of the circumcircle of IBC and the circle centered at I with radius IB
Ac = (IBC) /\ ((I,IC)-C)
ie the other than C intersection of the circumcircle of IBC and the circle centered at I with radius IC
Bc, Ba and Ca, Cb
A" = BcBa /\ CaCb
B" = CaCb /\ AbAc
C" = AbAc /\ BcBa
A'B'C' and A"B"C" are perspective. The perspector S is on the OI line, the internal center of similitude of (O) and (I) = X(55).
Ra = the radical axis of (IBC), (I,IA)
ie the radical axis of the circumcircle of IBC and the circle centered at I with radius IA.
Similarly Rb, Rc.
A* = AbAc /\ Ra
B* = BcBa /\ Rb
C* = CaCb /\ Rc
The triangles ABC, A*B*C* are perspective at a point P on the circumcircle of ABC.
The point is the center of the Jerabek hyperbola of the antipedal triangle of I (lying on the NPC of the antipedal of I = circumcircle of ABC)
Orthic triangle variation:
Internal center of similitude of circumcircle of orthic [=NPC of ABC] and incircle of orthic [=pedal circle of incenter of orthic = H of ABC] on the Euler line of ABC.
Perspector P lies on the NPC and is the center of the Jerabek hyperbola, X(125).
Antreas P. Hatzipolakis, 2 May 2013