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10918Feuerbach and pedal triangles

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  • Eric Danneels
    Dec 1, 2004
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      Dear Hyacinthians,

      in message 8533 I wrote:
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      The perpendiculars from each excenter to the line joining the
      Feuerbach point with the corresponding vertex of the medial triangle
      are concurrent.
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      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?
      ==> if we replace the Feuerbach point by another point is there
      another line, or is this property unique for the Feuerbach point ?

      I suppose it all has something to do with orthopoles since the
      Feuerbach point is the orthopole of the OI-line, but I can't find
      out why

      Greetings from Bruges

      Eric
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