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

Re: [EMHL] Orthologic?

Expand Messages
  • Randy Hutson
    Antreas, A B C , A^B^C^ are not orthologic.  However, A^B^C^ is perspective to ABC at X(262), and to A B C at non-ETC 43.220195027499022, which is also the
    Message 1 of 1 , Mar 5, 2013
    • 0 Attachment
      Antreas,

      A'B'C', A^B^C^ are not orthologic.  However, A^B^C^ is perspective to ABC at X(262), and to A"B"C" at non-ETC 43.220195027499022, which is also the center of the circumconic mentioned around post #21466, 1/30/2013.  Also, the centroid of A^B^C^ is the centroid of ABC, and the symmedian point of A^B^C^ = X(381);  X(69) of A^B^C^ = X(376); X(141) of A^B^C^ = X(549); X(193) of A^B^C^ = X(3543); and X(597) of A^B^C^ = X(5).

      A^B^C^ can be equivalently defined as:

      Let Pa be the parabola with focus A and directrix BC.  Let La be the polar of X(3) wrt Pa.  Define Lb, Lc cyclically.
      Let A^ = Lb/\Lc, B^ = Lc/\La, C^ = La/\Lb.

      Randy





      >________________________________
      > From: Antreas Hatzipolakis <anopolis72@...>
      >To: Hyacinthos <Hyacinthos@yahoogroups.com>
      >Sent: Saturday, March 2, 2013 4:29 PM
      >Subject: [EMHL] Orthologic?
      >
      >

      >I am wondering if these triangles are orthologic:
      >
      >Let A'B'C' be the cevian triangle of I, A"B"C" the medial
      >triangle, A*B*C* the circumcevian triangle of G wrt A"B"C",
      >and A^B^C^ the triangle bounded by the perpendiculars
      >to lines A"A*, B"B*, C"C* at A*,B*,C*, resp.
      >
      >Are the triangles A'B'C', A^B^C^ orthologic (as my figure shows)?
      >
      >APH
      >
      >
      >
      >

      [Non-text portions of this message have been removed]
    Your message has been successfully submitted and would be delivered to recipients shortly.