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9625Re: Two equivalent theorems (an old and a new(?))

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  • ben_goss_ro
    Apr 1, 2004
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      --- In Hyacinthos@yahoogroups.com, "Antreas P. Hatzipolakis"
      <xpolakis@o...> wrote:
      > Let ABC be a triangle, H its orthocenter and P a point.
      >
      > OLD THEOREM:
      > The reflections of the line HP in the sidelines of ABC concur
      > at P' on the circumcircle of ABC.
      >
      > NEW(?) THEOREM:
      > Let A', B', C' be the orthogonal projections of A,B,C on the line
      HP.
      > The reflections of AA', BB', CC' in the angle bisectors AA*, BB*,
      CC* (resp.)
      > of ABC concur at P' on the circumcircle of ABC.


      I'm sure the fact that the Simson line of P' is parallel to HP helps,
      but it's 4 AM here (in Romania), so I'm going to think it through
      tomorrow morning :).
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