Let ABC be a triangle and A1B1C1 is perspective with ABC at a point P and homothetic to ABC.
A2 is inversion of A1 respect to circumcircle of ABC. Define B2, C2 cyclically.
* Circumcenter of A2B2C2 lies on the line OP.
Application. Let P be a point on Euler line of ABC. A1,B1,C2 midpoints of AP, BP, CP resp.
A2 is inversion of A1 respect to circumcircle of ABC. Define B2, C2 cyclically.
** O',Circumcenter of A2B2C2 lies on the Euler Line of ABC.
For P=X(2), O'=X(33532)
For P=X(5), O'=X(?)
For P=X(20), O'=X(12084)
