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14758Θέμα: Re: [EMHL] Construction

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  • Nikolaos Dergiades
    Jan 14, 2007
    • 0 Attachment
      Dear Jean-Pierre,

      > [ND]
      > > > 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?
      >
      > [JPE]
      > > 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.
      [JPE]
      > A little explanation :
      > it is well known that the focii of the Steiner
      > circumellipse have
      > cevian of equal lengths.
      > As they lie on the Lucas cubic, their cevian
      > triangles are the pedal
      > triangles of the required points

      Excellent!
      Many thanks
      Friendly
      Nikos






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