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

21997TCS: P13

Expand Messages
  • Antreas
    Aug 16, 2013
      [Lozada]

      Let ABC be a triangle, A'B'C' the orthic triangle,
      A"B"C" the half-altitudes triangle (ie A",B",C"
      are the midpoints of the altitudes AA',BB',CC', resp.)
      and A*B*C* the Euler triangle (ie A*,B*,C* are the midpoints
      of AH,BH,CH, resp.).

      Denote:

      Ga,Gb,Gc = the centroids of A*B"C", B*C"A",C*A"B", resp.

      The triangles A'B'C', GaGbaGc are perspective.

      Perspector:

      X=
      (2*b^2*c^2-c^4-b^4+c^2*a^2+a^2*b^2)*(b^4-2*a^2*b^2+a^4-6*b^2*c^2-2*c^2*a^2+c^4)*\
      a : :
      (trilinears)

      X = cos(B-C)*(3-cos(2*A)) : : (trilinears)

      X =( 0.367623387808873, -0.24870103582042, 3.643169789255960 )

      X lies on line X(I),X(J) for these (I,J):

      (3,373), (5,51), (185,381), (389,3091), (394,3527), (511,3090), (546,1514),
      (568,5072), (569,1495), (575,1614), (578,1995), (1092,5020), (1173,5097),
      (1216,5055), (1656,3917), (1843,3542), (3060,5056), (3545,3567), (3819,5067),
      (5070,5447)

      Reference:
      Cesar Lozada, 16 Aug. 2013,
      http://tech.groups.yahoo.com/group/Anopolis/message/831