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22081Pedal/antipedal triangles loci

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  • Antreas Hatzipolakis
    Mar 28 11:59 PM
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      Let ABC be a triangle, P a point, A'B'C', A"B"C" the pedal, antipedal
      triangles of P, resp.

      Denote:

      A* =  B'C" /\ C'B", B* = C'A" /\ A'C", C* = A'B" /\ B'A"


      Which is the locus of P such that the triangle A*B*C* is perspective with
      the triangles (1) ABC, (2) A'B'C' (3) A"B"C"  ?

      Note: For P = I the circumcenter of A*B*C* is the I.
      Reference:
      http://problems.ru/view_problem_details_new.php?id=64357

      APH