I just remember the Faure theorem.

A triangle ABC is autopolar wrt the conic Gamma iff the ABC-circumcircle is

orthogonal to the orthoptic circle of Gamma.

Friendly

Francois

On Fri, Jul 2, 2010 at 8:15 PM, Barry Wolk <wolkbarry@...> wrote:

>

>

> > From: jpehrmfr <jean-pierre.ehrmann@...<jean-pierre.ehrmann%40wanadoo.fr>

> >

>

> >

> > Dear Barry

> > [Barry Wolk]

> > > Some computation shows that for any circle that meets

> > the 2 sides AB and AC harmonically, its center lies on the

> > perpendicular bisector of BC.

> >

> > I don't agree with you. Your circles are member of the

> > pencil with Poncelet points (circles with radius 0) A and

> > the projection of A upon BC.

> > Friendly. Jean-Pierre

>

> I finally realized that I used an incorrect formula for harmonic

> conjugates, namely (BP/PC)*(BQ/QC)=-1, instead of the correct

> (BP/PC)/(BQ/QC)=-1 when P,Q are harmonic conjugates wrt B,C. So my results

> apply to this strange kind of "conjugates," but not to harmonics.

> --

> Barry Wolk

>

>

>

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