ANOPOLIS 9768

[APH]:

 

An interesting triangle defined by Angel:

Let ABC be  triangle and IaIbIc the antipedal triangle of I.

Denote:

V = the circumcenter of IaIbIc = Bevan point X(40)

Va, Vb, Vc = the antipodes of V in the the circumcircles of VBC, VCA, VAB, resp.

Let's call VaVbVc as the "Bevan antipodal triangle".

ABC, VaVbVc are perspective at X(57)
Angel Montesdeoca,  HG141019

I think that they are orthologic too.

Which triangles of ABC are perspective/orthologic/parallelogic. etc  with VaVbVc ?

 

 

[Randy Hutson]

 

This construction can be generalized for an arbitrary point P (instead of V), and is, in fact, the antipedal triangle of P.

 

Best regards,

Randy