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

Locus, Poncelet Point

Expand Messages
  • Antreas
    Let ABC be a triangle, P a point, and (Op) the cevian circle of P (with center Op). Which is the locus of P such that the Poncelet point of Op (ie the point of
    Message 1 of 1 , Apr 18, 2013
    • 0 Attachment
      Let ABC be a triangle, P a point, and (Op) the
      cevian circle of P (with center Op).

      Which is the locus of P such that the Poncelet point of Op
      (ie the point of concurrence of the NPCs of OpBC, OpCA,
      OpAB) lies on the cevian circle (Op) ?

      Obviously G, H are on the locus.

      For P = I, we have that the circles
      Cevian_I, Pedal_I, NPC_ABC concur at Feuerbach point,
      and the circles NPC_ABC, NPC_OpBC, NPC_OpCA, NPC_OpAB
      concur at Poncelet point of Op
      If the Poncelet point of Op lies on (Op) [= the cevian circle
      of I], then the Poncelet point of Op coincides with
      the Feuerbach point.


      Antreas
    Your message has been successfully submitted and would be delivered to recipients shortly.