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[EMHL]] Happy New Year

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  • Ricardo Barroso
    Happy New year 2013 . From Sevilla  Ricardo http://personal.us.es/rbarroso/trianguloscabri/ [Non-text portions of this message have been removed]
    Message 1 of 14 , Jan 2, 2013
      Happy New year 2013 .

      From Sevilla 

      Ricardo

      http://personal.us.es/rbarroso/trianguloscabri/

      [Non-text portions of this message have been removed]
    • Bernard Gibert
      Dear all, If A B C is the pedal triangle of P (instead of cevian triangle of P), and A , B , C as before, If A* is the homothetic of A under h(A , k), B*
      Message 2 of 14 , Jan 2, 2013
        Dear all,

        If A'B'C' is the pedal triangle of P (instead of cevian triangle of P), and A", B", C" as before,

        If A* is the homothetic of A" under h(A', k), B* and C* likewise, then the locus of P such that ABC and A*B*C* are perspective (at X) is a central cubic passing through X3 with asymptotes parallel to the altitudes of ABC and concurring on the Brocard axis, very similar to the Darboux cubic which is obtained when k = 0.

        The locus of the perspector X is pK(X2, T) where

        T = (-a^4+b^4+c^4)k-4 SA Sw : : , on the line X4-X69.

        If k = 0, T = X69 and this is the Lucas cubic.

        Best regards

        Bernard

        [Non-text portions of this message have been removed]
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