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17959CONJECTURE (Re: More Reflections in bisectors)

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  • xpolakis
    Jul 4, 2009
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      [APH]
      > Let ABC be a triangle, A'B'C' its medial triangle
      > and P a point.
      >
      > 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 ?
      >
      > It seems the locus is the entire plane.
      >
      > Parallelogic centers?

      It is true and simple, since ABC, A'B'C'
      are homothetic.

      How about if A'B'C' is the orthic triangle?

      Which is the locus of P?

      Antreas
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