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21999TCS: P15

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  • Antreas
    Aug 24, 2013
      [Hatzipolakis - Montesdeoca]

      [APH]
      Let ABC be a triangle and A'B'C' the medial triangle.

      Denote:

      Obc, Ocb = the circumcenters of BCB', BCC', resp.

      Ma = the midpoint of ObcOcb

      Similarly Mb, Mc.

      The centroid of MaMbMc lies on the Euler line of ABC

      [AM]
      Barycentric coordiantes of the centroid of MaMbMc:

      (2 SB SC + 11 a^2SA : 2 SC SA + 11 b^2 SB : 2 SA SB + 11 c^2 SC)

      Reference:

      http://tech.groups.yahoo.com/group/Anopolis/message/873
      Sat Aug 24, 2013