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17960Re: [EMHL] CONJECTURE (Re: More Reflections in bisectors)

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  • Nikolaos Dergiades
    Jul 4, 2009
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      Dear Antreas,

      > [APH]
      > > Let La, Lb, Lc be the reflections of PA', PB', PC'
      > > in the bisectors AI, BI, CI, resp.
      > >
      > > Which is the locus of P such that the triangles
      > > ABC, Triangle bounded by (La, Lb, Lc) are
      > > parallelogic ?
      > >
      > How about if A'B'C' is the orthic triangle?
      > Which is the locus of P?
      > Antreas

      The locus is the linf +
      the conic with center X(1112)
      that passes through the vertices of the cevian
      triangles of X(4) Orthocenter and
      X(648) the trillinear pole of Euler line.
      See the notes in ETC for X(1112).

      Best regards

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