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

Locus

Expand Messages
  • Antreas Hatzipolakis
    Let ABC be a triangle, P a point and A B C the 1. cevian 2. the pedal triangle of P. Denote: Ab = (Parallel to AB through B ) / BC Ac = (Parallel to AC
    Message 1 of 235 , Mar 20, 2013
    • 0 Attachment
      Let ABC be a triangle, P a point and A'B'C' the 1. cevian 2. the pedal
      triangle of P.

      Denote:

      Ab = (Parallel to AB through B') /\ BC
      Ac = (Parallel to AC through C') /\ BC
      Aa = (Parallel to AB through B') /\ (Parallel to AC through C')

      Similarly:

      Bc = (Parallel to BC through C') /\ CA
      Ba = (Parallel to BA through A') /\ CA
      Bb = (Parallel to BC through C') /\ (Parallel to BA through A')

      Ca = (Parallel to CA through A') /\ AB
      Cb = (Parallel to CB through B') /\ AB
      Cc = (Parallel to CA through A') /\ (Parallel to CB through B')

      A* = AbBb /\ AcCc, B* = BcCc /\ BaAa, C* = CaAa /\ CbBb

      Which is the locus of P such that:

      1. ABC, A*B*C*

      2. A'B'C', A*B*C*

      are perspective?

      Variations:

      A* = AbCc /\ AcBb, B* = BcAa /\ BaCc, C* = CaBb /\ CbAa


      Antreas
    • Antreas Hatzipolakis
      Let ABC be a triangle and P a point Which is the locus of P such that PA + PB + PC = 0 (signed segments) ? APH PS see special case
      Message 235 of 235 , Apr 10
      • 0 Attachment
        Let ABC be a triangle and P a point

        Which is the locus of  P such that PA + PB + PC = 0
        (signed segments) ?

        APH

        PS see special case

        https://www.facebook.com/photo.php?fbid=811391552270276&set=p.811391552270276&type=1&theater
      Your message has been successfully submitted and would be delivered to recipients shortly.