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9881Re: [EMHL] The Brocard points of a quadrilateral (Geoff Millin)

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  • jpehrmfr
    Jun 8, 2004
      Dear Alexey
      > I have a next hypothesis. Let A_1...A_n is the cyclic polygon. Then
      > 1) The Brocard points exist iff the symmedians of triangles
      > A_{i-1}A_iA_{i+1} from A_i concur in point L.
      > 2) Two Brocard points P, Q are in the circle with diameter OL and
      the angles
      > POL and QOL are equal to brocard angle.
      > If 1) is correct then I can prove 2)

      And what do you think of the following conjecture :
      A cyclic polygon has Brocard points if and only if the polygon is
      the inverse of a regular polygon?
      Friendly. Jean-Pierre
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