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14755Θέμα: Re: [EMHL] Construction

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  • Nikolaos Dergiades
    Jan 14, 2007
      Dear Bernard,

      > > [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?

      Friendly
      Nikos Dergiades







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