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6240Re: Some theorems on Miquel points

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  • jpehrmfr <jean-pierre.ehrmann@wanadoo.fr>
    Jan 1, 2003
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      Dear Darij

      > 2. Let Ma, Mb, Mc be the centers of the circles AB'C', BC'A',
      CA'B'
      > [it is well-known that triangles MaMbMc and ABC are similar], let
      M'
      > be the circumcenter of triangle MaMbMc, and M the circumcenter of
      > triangle ABC. Then M'M = M'P.
      >
      > [This is a theorem by Peter Baum; proposed in the little German
      > periodical "Die Wurzel" (see the website wurzel.org), in the 12/98
      > issue. Solved by Sefket Arslanagic in the 5/99 issue; the solution
      > was quite involved.]

      It is well known (Steiner 1827) that Ma,Mb,Mc,M,P are concyclic
      (Miquel cirle of the quadrilateral). Hence, this theorem is not a
      recent one.
      Happy new year to all Hyacinthists. Jean-Pierre
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