10977RE: [EMHL] circumcevian reflections
- Jan 6, 2005Dear Bernard,
> > [FvL]To start the new year let me offer a little theorem:[BG]
> > 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.
> your point is the isogonal conjugate of the infinite point of theThanks, Bernard!
> 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.
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
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