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17952Re: More Reflections in bisectors

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  • xpolakis
    Jul 2, 2009
      Let ABC be a triangle and P = (x:y:z) a point.

      Denote:

      A* :=(Perpendicular from B to CP) /\ (Perpendicular from C in BP)

      B* :=(Perpendicular from C to AP) /\ (Perpendicular from A to CP)

      C* :=(Perpendicular from A to BP) /\ (Perpendicular from B to AP)

      [The triangles A*BC, B*CA, C*AB share the same Orthocenter P]

      Oa := The Circumcenter of A*BC
      Ob := The Circumcenter of B*CA
      Oc := The Circumcenter of C*AB

      P* := The Point of Concurrence of the Circumcircles
      of A*BC, B*CA, C*AB
      [We have seen recently this point in Hyacinthos]

      La := The Reflection of P*Oa in AI

      Lb := The Reflection of P*Ob in BI

      Lc := The Reflection of P*Oc in CI

      I think that for P = I the lines La, Lb, Lc are
      concurrent. Point?

      In general, which is the locus of P such that the La,Lb,Lc
      are concurrent?


      Antreas
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