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9146Cyclic quadrilateral problem

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  • Darij Grinberg
    Jan 28, 2004
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      Please help me with the following problem (I need it as
      a lemma):

      Given a cyclic quadrilateral ABCD with the circumcenter
      O. The perpendicular to BD through B meets the
      perpendicular to AC through C at E. The perpendicular
      to BD through D meets the perpendicular to AC through A
      at F. Finally, let X be the intersection of the lines
      AB and CD. Then, the points O, E, F, X are collinear.

      Well, it is easy to show that O is the midpoint of EF;
      hence, O, E, F are collinear, but how about X ?

      Thanks!
      Sincerely,
      Darij Grinberg
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