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9886Re: The Brocard points of a quadrilateral (typo)

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  • jpehrmfr
    Jun 9, 2004
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      Dear Alexey,
      I wrote
      > suppose that ABC is a variable isosceles triangle (in B) inscribed
      > in a fixed circle with center o; let M be a fixed point and A'B'C'
      > the cevian triangle of M wrt ABC.

      Of course, I was meaning the circumcevian triangle of M wrt ABC.
      Sorry for the typo.

      > It is very easy to check that the
      > B'-symedian of A'B'C' intersects the line OM at a point L
      > independant of the choice of ABC.
      > If S is a point of the circle such as OM and OS are perpendicular,
      L
      > is the projection upon OM of the reflection of O wrt SM. More over
      L
      > lies on the half-line OM and inside the circle.
      > From this it follows that if B_1,...,B_n is a regular polygon
      > inscribed in the circle, if A_k is the second intersection of MB_k
      > with the circle, every A_k symedian of A_(k-1),A_k,A_(k+) goes
      > through L.
      > That's probably a part of the proof you're waiting for.
      > Friendly. Jean-Pierre
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