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

Tangent NPCs / Incircles

Expand Messages
  • Antreas
    1. The NPC(antipedal_of_O) is tangent to Incircle(antipedal_of_O) = = Circumcircle(ABC) = NPC(antipedal_of_H) [Feuerbach point of antipedal_of_O] 2. The
    Message 1 of 2 , Mar 19, 2013
      1. The NPC(antipedal_of_O) is tangent to Incircle(antipedal_of_O) =
      = Circumcircle(ABC) = NPC(antipedal_of_H)
      [Feuerbach point of antipedal_of_O]

      2. The Incircle(antipedal_of_O) = Circumcircle(ABC) =
      = NPC(antipedal_of_H) is tangent to Incircle(antipedal_of_H)
      [Feuerbach point of antipedal_of_H]

      Generalizations:

      Let ABC be a triangle, P,P* two isogonal conjugate points
      and A'B'C',A"B"C" the antipedal triangles of P,P*, resp.

      Which is the locus of P such that:

      1. the NPC(A'B'C') is tangent to NPC(A"B"C")

      2. the Incircle(A'B'C') is tangent to Icircle(A"B"C")

      McCay cubic + (O) + Linf + ???????????????????????????

      APH
    • Francisco Javier
      I get K003 (McCay cubic) and K024 for tangents NPCs.
      Message 2 of 2 , Mar 19, 2013
        I get K003 (McCay cubic) and K024 for tangents NPCs.

        --- In Hyacinthos@yahoogroups.com, "Antreas" <anopolis72@...> wrote:
        >
        > 1. The NPC(antipedal_of_O) is tangent to Incircle(antipedal_of_O) =
        > = Circumcircle(ABC) = NPC(antipedal_of_H)
        > [Feuerbach point of antipedal_of_O]
        >
        > 2. The Incircle(antipedal_of_O) = Circumcircle(ABC) =
        > = NPC(antipedal_of_H) is tangent to Incircle(antipedal_of_H)
        > [Feuerbach point of antipedal_of_H]
        >
        > Generalizations:
        >
        > Let ABC be a triangle, P,P* two isogonal conjugate points
        > and A'B'C',A"B"C" the antipedal triangles of P,P*, resp.
        >
        > Which is the locus of P such that:
        >
        > 1. the NPC(A'B'C') is tangent to NPC(A"B"C")
        >
        > 2. the Incircle(A'B'C') is tangent to Icircle(A"B"C")
        >
        > McCay cubic + (O) + Linf + ???????????????????????????
        >
        > APH
        >
      Your message has been successfully submitted and would be delivered to recipients shortly.