Dear Bernard,

> > [FvL]To start the new year let me offer a little theorem:

> >

> > If A'B'C' is a circumcevian triangle [of point P], and A"B"C" are the

> > reflections of

> > A'B'C' through the sides of ABC, then the circles (ABC), (A"B"C),

> > (A"BC")

> > and (AB"C") are concurrent in one point.

[BG]

> your point is the isogonal conjugate of the infinite point of the

> direction which is perpendicular to HP.

>

> notice that ABC and A"B"C" are perspective iff P lies on the Jerabek

> hyperbola or at infinity.

Thanks, Bernard!

The locus of the perspector for P on the Jerabek hyperbola is a quartic, the

isogonal conjugate of the conic

SUM b^4c^4SA(b^2-c^2)^4x^2 + a^6b^2c^2(c^2-a^2)^2(a^2-b^2)^2yz = 0

cyclic

Kind regards,

Floor.