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

TCS: P3, P4, P5

Expand Messages
  • Antreas
    P3: [Grinberg - Hatzipolakis - Moses]: Description (barycentrics): The reflections of the Brocard axes (OK lines) of the triangles GBC, GCA, GAB in BC, CA, AB,
    Message 1 of 1 , Jul 18, 2013
    • 0 Attachment
      P3: [Grinberg - Hatzipolakis - Moses]:

      Description (barycentrics):

      The reflections of the Brocard axes (OK lines) of the triangles
      GBC, GCA, GAB in BC, CA, AB, resp. are concurrent.

      Coordinates:
      a^2 (49 a^8 - 133 a^6 b^2 + 120 a^4 b^4 - 29 a^2 b^6 -
      7 b^8 - 133 a^6 c^2 + 21 a^4 b^2 c^2 + 69 a^2 b^4 c^2 +
      23 b^6 c^2 + 120 a^4 c^4 + 69 a^2 b^2 c^4 - 48 b^4 c^4 -
      29 a^2 c^6 + 23 b^2 c^6 - 7 c^8) : :

      Search number -1.9912192905485415

      P4,P5: [Hatzipolakis - Moses]:

      Description:

      The reflections of the Brocard axes of GBC,GCA,GAB in the
      respective sidelines of:

      (1) Medial Triangle
      (2) Antimedial Triangle of ABC

      are concurrent.

      Coordinates (barycentrics):

      (1):
      (-28 a^10 + 58 a^8 b^2 - 39 a^6 b^4 + 95 a^4 b^6 - 149 a^2 b^8 + 63 b^10 + 58
      a^8 c^2 + 6 a^6 b^2 c^2 + 21 a^4 b^4 c^2 + 64 a^2 b^6 c^2 - 189 b^8 c^2 - 39 a^6
      c^4 + 21 a^4 b^2 c^4 + 138 a^2 b^4 c^4 + 126 b^6 c^4 + 95 a^4 c^6 + 64 a^2 b^2
      c^6 + 126 b^4 c^6 - 149 a^2 c^8 - 189 b^2 c^8 + 63 c^10) :: SEARCH =
      7.5521575344053693459 .. not in ETC.

      (2):

      (-77 a^10 + 191 a^8 b^2 - 159 a^6 b^4 + 124 a^4 b^6 - 142 a^2 b^8 + 63 b^10 +
      191 a^8 c^2 - 15 a^6 b^2 c^2 - 48 a^4 b^4 c^2 + 41 a^2 b^6 c^2 - 189 b^8 c^2 -
      159 a^6 c^4 - 48 a^4 b^2 c^4 + 186 a^2 b^4 c^4 + 126 b^6 c^4 + 124 a^4 c^6 + 41
      a^2 b^2 c^6 + 126 b^4 c^6 - 142 a^2 c^8 - 189 b^2 c^8 + 63 c^10) :: SEARCH =
      17.095534359359280017

      REFERENCE:
      http://tech.groups.yahoo.com/group/Anopolis/message/117
    Your message has been successfully submitted and would be delivered to recipients shortly.