HYACINTHOS 6321

Dear Darij and Jean-Pierre,

[DG]:

> > Prof. Clark Kimberling has updated ETC, as we have seen. But there
> > are still some points whose trilinears we don't know - especially
> I
> > with my knowledge on trilinears which doesn't go further than line
> > equations. I am interested in the trilinears of the Schröder
> point.

[JPE]:

> Your point is trilinear x = (b-c)^2 + a(b+c-2a)
> Friendli. Jean-Pierre

It seems that there are more points P satisfying the
condition that if A'B'C' is the pedal triangle of P, then the
circumcircles of AA'P, BB'P and CC'P meet in a second point. The
circumcenter seems to be one of these points. Perhaps the locus is the
Stammler hyperbola? I am now running out of time, later I will invest
more time.

Kind regards,
Sincerely,
Floor Van Lamoen