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Orhologic again

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  • xpolakis
    Let ABC be a triangle, and HaHbHc, MaMbMc the pedal triangles of H,O, resp. Let A B C be the circumcevian triangle of O in the NPC wrt triangle HaHbHc, and
    Message 1 of 1 , Apr 30, 2009
      Let ABC be a triangle, and HaHbHc, MaMbMc
      the pedal triangles of H,O, resp.

      Let A'B'C' be the circumcevian triangle of O
      in the NPC wrt triangle HaHbHc, and A"B"C"
      the circumcevian triangle of H wrt MaMbMc
      (ie A' is the other [than Ha] intersection
      of OHa with the NPC, and A" is the other
      [than Ma] intersection of HMa with the NPC, etc)

      I think that the triangles:

      ABC, Triangle bounded by (A'A",B'B",C'C")
      are orthologic. Orthologic centers?

      Locus:

      Let ABC be a triangle, and PaPbPc, QaQbQc
      the pedal triangles of two isogonal
      conjugate points P, P*, resp.

      Let A'B'C' be the circumcevian triangle of P*,
      in the pedal circle of P,P*, wrt triangle PaPbPc,
      and A"B"C"the circumcevian triangle of P wrt QaQbQc.
      (ie A' is the other [than Pa] intersection
      of P*Pa with the pedal circle, and A" is the other
      [than Qa] intersection of PQa with the pedal circle, etc)

      Which is the locus of P such that the triangles:
      ABC, Triangle bounded by (A'A",B'B",C'C")
      are orthologic ?

      APH
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