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22478CONJECTURE with PRIZE :-)

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  • Antreas Hatzipolakis
    Jun 29, 2014
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      I offer an old book in German on Triliner Coordinates.

      Well ... it is available on-line, but it is an other thing to have in your
      library the original copy and other thing to have an electronic copy :-)

      Now about the conjecture:

      A way to prove it is to find the locus of points with
      the property in question.

      That is:

      Let ABC be a triangle and P a point.
      La, Lb, Lc = the Euler lines of PBC,PCA,PAB, resp.
      Na, Nb, Nc = the NPC centers of PBC,PCA, PAB, resp.
      The perpendicular to La at Na intersects BC,CA,AB at Aa, Ab,Ac,
      A' = BAb /\ CAc. Similarly B',C'.

      Which is the locus of P such that ABC, A'B'C' are perspective?
      (or, equivalently, Aa, Bb, Cc are collinear?)

      If part of the locus is the Neuberg Cubic, then the conjecture
      is proved true !


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