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22167Orthologic centers

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  • Antreas Hatzipolakis
    Apr 21, 2014
    • 0 Attachment
      Let ABC be a triangle and IaIbIc the antipedal triangle of I (excentral triangle).

      Denote:

      A'B'C' = the medial triangle of ABC

      A1B1C1 = the medial triangle of IaIbIc

      A2B2C2 = the medial triangle of A1B1C1

      Ma,Mb,Mc = the midpoints of A'A2, B'B2, C'C2

      1, ABC, A2B2C2 are orthologic.
      The orthologic center (ABC,A2B2C2) is the I.
      The other one ?  (on the OI line)

      2. ABC, MabMc are orthologic
      Orthologic centers ? (one is on the OI line)

      APH