Loading ...
Sorry, an error occurred while loading the content.

17836Re: A configuration

Expand Messages
  • xpolakis
    Jun 3, 2009
    • 0 Attachment
      [APH]
      > > Let ABC be a triangle and A'B'C' the orthic triangle.
      > >
      > > Denote:
      > >
      > > Lab := The Reflection of BB' in AA'
      > > Mab := The Parallel to Lab through C.
      > >
      > > Lac := The Reflection of CC' in AA'
      > > Mac := The Parallel to Lac through B.
      > >
      > > A* := Mab /\ Mac
      > >
      > > Similarly B*,C*.

      > > 5. Let Na, Nb, Nc be the NPC centers of the triangles
      > > A*BC, B*CA, C*AB, resp.
      > > The triangles ABC, NaNbNc are perspective.
      > > Perspector?

      [JPE]
      > If U=X(54) is the isogonal conjugate of N and
      > V=X(140)=midpoint(ON), the perspector is P=-3U+4V
      > (this point lies on the line through the Lemoine point and
      > the two Corsican Imperial points)

      EQUIVALENTLY:

      Let ABC be a triangle, A1B1C1 the circumcevian triangle
      of H, and M1M2M3 the Medial triangle of ABC.

      Let A*,B*,C* be the reflections
      of A1,B1,C1 in M1,M2,M3, resp. (symmetric points)

      Let Na, Nb, Nc be the NPC centers of the triangles
      A*BC, B*CA, C*AB, resp.
      The triangles ABC, NaNbNc are perspective.


      APH
    • Show all 5 messages in this topic