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Menelaus Theorem extended

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  • Antreas
    Let ABC be a triangle. A conic intersects sidelines BC at A1, A2, CA at B1, B2 and AB at C1, C2. Theorem: (BA1 / CA1) * (BA2 / CA2) * (CB1 / AB1) * (CB2 / AB2)
    Message 1 of 1 , Apr 16, 2013
      Let ABC be a triangle. A conic intersects sidelines
      BC at A1, A2, CA at B1, B2 and AB at C1, C2.

      Theorem:

      (BA1 / CA1) * (BA2 / CA2) *

      (CB1 / AB1) * (CB2 / AB2) *

      (AC1 / BC1) * (AC2 / BC2) = 1


      Reference:
      Emm. Damigos: Extension of the Theorem of Menelaus.
      Euclid (=Greek math. periodical) Nov. 1968, pp. 114-8,
      May 1969 p. 389-392

      APH
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