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antiparallels (cubic)

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  • Antreas P. Hatzipolakis
    Let ABC be a triangle, P a point and HaHbHc the orthic triangle of ABC. Let La, Lb, Lc be the parallels to HbHc, HcHa, HaHb resp. through P. Lab = La / AB,
    Message 1 of 1 , Nov 1, 2003
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      Let ABC be a triangle, P a point and HaHbHc the
      orthic triangle of ABC.

      Let La, Lb, Lc be the parallels to HbHc, HcHa, HaHb
      resp. through P.

      Lab = La /\ AB, Lac = La /\ AC

      Ab = Orthogonal Projection of Lab on PPa

      Ac = Orthogonal Projection of Lac on PPa

      A' = BAb /\ CAc. Similarly B', C'.

      Which is the locus of P such that ABC, A'B'C' are perspective?


      Antreas

      PS. I found a cubic whose the equation has the xyz term,
      but I don't know if decomposes or not.

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