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Re: [EMHL] Re: Perspective?

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  • Antreas Hatzipolakis
    One more.... HaHbHc = the orthic triangle. (N1) = the circle (Ha, HaN) ie the circle with center Ha and radius HaN =R/2 Similarly (N2),(N3) A B C = the
    Message 1 of 23 , Feb 20, 2013
      One more....

      HaHbHc = the orthic triangle.
      (N1) = the circle (Ha, HaN) ie the circle with center Ha and radius HaN =R/2
      Similarly (N2),(N3)

      A'B'C' = the triangle bounded by the radical axes of
      ((O),(N1)),((O),(N2)),((O),(N3)).

      Are the triangles HaHbHc, N1N2N3 perspective?

      aph


      On Wed, Feb 20, 2013 at 1:29 PM, Antreas <anopolis72@...> wrote:

      > **
      >
      >
      > I am not sure If I have already posted this:
      >
      > Let ABC be a triangle, (N1),(N2),(N3) the reflections of
      > (N)[=NPC] in OA,OB,OC, resp. and A'B'C' the triangle bounded
      > by the radical axes of ((O),(N1)),((O),(N2)),((O),(N3)).
      >
      >
      > Are N1N2N3, A'B'C' perspective?
      >
      > APH
      >
      > __
      >


      [Non-text portions of this message have been removed]
    • Antreas Hatzipolakis
      Let ABC be a triangle with excenters Ia,Ib,Ic. The NPC of AHIa interscts the excircle (Ia) at A other than the Feuerbach point Fa. The NPC of BHIb
      Message 2 of 23 , May 6, 2014

        Let ABC be a triangle with excenters Ia,Ib,Ic.

        The NPC of  AHIa interscts the excircle (Ia) at A' other than the
        Feuerbach point Fa.

        The  NPC of  BHIb intersects the excircle (Ib) at B' other than the
        Feuerbach point Fb,

        The  NPC of  CHIc intersects the excircle (Ic) at C' other than the
        Feuerbach point Fc.

        Are the triangles ABC, A'B'C' perspective?

        In any case, has the triangle A'B'C' any interesting properties?

        APH

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