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10920Re: [EMHL] Feuerbach and pedal triangles

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  • Paul Yiu
    Dec 1, 2004
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      Dear Eric,

      [ED]: I conjecture the following generalization:

      >Let O be the circumcenter and I the incenter
      >The perpendiculars from each excenter to the line joining the
      >Feuerbach point with the corresponding vertex of the pedal triangle
      >of any point on OI are concurrent.
      >
      >The following questions intrigue me:
      >
      >==> what is the locus of the perspectors ?
      >==> is OI the only set of points with this property?

      Apart from the OI line, there is also the line containing X(36) and its
      isogonal conjugate X(80).
      X(36) is the inversive image of I in the circumcircle.

      Best regards
      Sincerely
      Paul



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