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19140Re: [EMHL] Re: Harmonic Conic

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  • Francois Rideau
    Jul 29, 2010
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      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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