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17953Re: More Reflections in bisectors

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  • garciacapitan
    Jul 2, 2009
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      For P = I the concurrence point is the same point L that in Hyacinthos message #17947


      --- In Hyacinthos@yahoogroups.com, "xpolakis" <anopolis72@...> wrote:
      >
      > 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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