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Locus (Re: X(54))

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  • Antreas
    Generalization: Let ABC be a triangle, P a point, P1, P2, P3 the reflections of P in BC, CA, AB, resp., P12, P13 the reflections of P1 in in AC, AB, resp.,
    Message 1 of 3 , Dec 5, 2011
      Generalization:

      Let ABC be a triangle, P a point, P1, P2, P3 the reflections of
      P in BC, CA, AB, resp., P12, P13 the reflections of P1 in in AC, AB,
      resp., P21, P23 the reflections of P2 in BC, BA, resp. and P31, P32
      the reflections of P3 in CB, CA, resp.

      Which is the locus of P such that the perpendicular bisectors
      of P12P13, P21P2, P31P32 are concurrent?

      APH


      --- In Hyacinthos@yahoogroups.com, Antreas Hatzipolakis <anopolis72@...> wrote:
      >
      > A construction of X(54)
      >
      > http://anthrakitis.blogspot.com/2011/12/reflections-of-circumcircle-in.html
      >
      > APH
    • Francisco Javier
      The locus is Neuberg cubic. The locus of points of intersection is K073, the inverse of Neuberg cubic in circumcircle. Best regards, Francisco Javier.
      Message 2 of 3 , Dec 5, 2011
        The locus is Neuberg cubic.

        The locus of points of intersection is K073, the inverse of Neuberg cubic in circumcircle.


        Best regards,
        Francisco Javier.


        --- In Hyacinthos@yahoogroups.com, "Antreas" <anopolis72@...> wrote:
        >
        > Generalization:
        >
        > Let ABC be a triangle, P a point, P1, P2, P3 the reflections of
        > P in BC, CA, AB, resp., P12, P13 the reflections of P1 in in AC, AB,
        > resp., P21, P23 the reflections of P2 in BC, BA, resp. and P31, P32
        > the reflections of P3 in CB, CA, resp.
        >
        > Which is the locus of P such that the perpendicular bisectors
        > of P12P13, P21P2, P31P32 are concurrent?
        >
        > APH
        >
        >
        > --- In Hyacinthos@yahoogroups.com, Antreas Hatzipolakis <anopolis72@> wrote:
        > >
        > > A construction of X(54)
        > >
        > > http://anthrakitis.blogspot.com/2011/12/reflections-of-circumcircle-in.html
        > >
        > > APH
        >
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