- Dear Antreas,

> [BG]:

there are several such points on the McCay cubic. at most 4 real?, at

> >consider the circumcenters O1 and O2 of the pedal and antipedal

> >triangles of a point P.

> >for which P do O1 and O2 coincide ?

>

> [APH] Nice problem!!

> If P is real, then it lies on the McCay cubic.

> Now, no one of the simple centers on McCay (ie O,H,I) has

> this property.

> So, we have a new center on the McCay cubic???

least 2 real?

I didn't find a construction for them but I suspect they are only

conic-constructible.

Jean-Pierre, help...

Best regards

Bernard

[Non-text portions of this message have been removed] - Dear Bernard and Antreas,

[BG]: consider the circumcenters O1 and O2 of the pedal and antipedal

triangles of a point P. For which P do O1 and O2 coincide ?

*** I have a problem related to antipedal triangles.

By calculations, the antipedal triangle of P and the circumcevian

triangle of Q are perspective if and only if O, P, Q are collinear.

Is it possible to give a synthetic proof?

Best regards

Sincerely

Paul