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13487Re: [EMHL] Mittenpunkt And Concurrency Of Three Euler Lines

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  • Antreas P. Hatzipolakis
    Jul 1, 2006
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      Dear Tuan

      > I have got a very nice first result:
      > - Q is fixed and is incenter I
      > - Line is OH
      > The locus (or at least all points on this line) is line connected
      > mittenpunkt and Gergonne point.

      That is,

      Let ABC be a triangle, and P a point.
      The perpendicular to IA through P intersects AB,AC at Ab,Ac, resp.
      Similarly Bc,Ba, and Ca,Cb.

      The locus of P such that the OH lines (Euler Lines) of PBcCb, PCaAc, PAbBa
      are concurrent is Mittenpunkt-Gergone Line + ???

      Probably the complete locus is some Cubic = Conic + Line

      Nice result, indeed!

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