ADGEOM 5185

Dear friends, 

 

I introduce  four new points on Euler line: 

 

I found these points trying to solve a problem proposed by Kadir Altintas.

 

Given a triangle ABC and a point P, call DEF its circuncevian triangle. The circumcenters of six triangles PBD, PDC, PCE, PEA, PAF and PFB lie on the same conic. When this conic is a circle?

 

Reference:

http://garciacapitan.blogspot.com/2019/02/four-points-on-euler-line.html

 

Best regards,

Francisco Javier Garcia Capitan.