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11785Re: More 3D centers

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  • Hauke Reddmann
    Dec 3, 2005
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      --- In Hyacinthos@yahoogroups.com, "jpehrmfr" <Jean-
      Pierre.Ehrmann.70@n...> wrote:
      >
      > To be more precise, if l = (ua+vb-wc)(-ua+vb+wc)(ua-vb+wc)
      > If l>0 then Q,Q' are real and distinct; thus the locus of P is the
      > circle above
      > If l=0 then Q=Q' and the locus of P is the line perpendicular at Q
      > to the plane ABC
      > If l<0, a point P such as PA:PB:PC = u:v:w cannot exist
      >
      I prefer to replace "cannot exist" by "does not lie in
      real space"; I encountered many geometrical problems
      where e.g. a locus is imaginary except one special real point.
      Also, I don't shriek back from using negative or imaginary
      distances inbetween if it gives a cute result :-)

      THX for verifying it's a circle - where (projected back on ABC)
      does its highest/lowest point lie?

      Hauke
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