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14756ÈÝìá: Re: [EMHL] Construction

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  • jpehrmfr
    Jan 14, 2007
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      Dear Nikolaos
      > > > [ND] How can we construct the two lines
      > > > given by the equation in barycentrics:
      > > >
      > > > CyclicSum (SA*SA*(SB-SC)xx + 2SB*SC*(SB-SC)yz) = 0
      >
      > [BG]
      > > these are the parallels at H to the asymptotes of
      > > the Kiepert hyperbola.
      >
      > Thank you very much.
      > These are the parallels from H to the Simson
      > lines of the points where the Brocard axis meets
      > the circumcircle.
      >
      > I tried to find for which points P the pedal triangle
      > of P A'B'C' has vertices equidistant from A,B,C
      > i.e. AA' = BB' = CC'.
      > These points must be symmetric wrt H.
      > I found that these points must be on these lines.
      > From a sketch it seems to exist only two such points
      > on one of these lines.
      > Can we construct these points?


      Your points are the homothetic of the focii of the Steiner
      circumellipse in (L,3/2) where L = de Longchamps point.
      For both points, AA' = 3.T/2 where T = semimajor axis of the ellipse.

      Friendly. Jean-Pierre
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