6240Re: Some theorems on Miquel points
- Jan 1, 2003Dear 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], letM'
> be the circumcenter of triangle MaMbMc, and M the circumcenter ofIt is well known (Steiner 1827) that Ma,Mb,Mc,M,P are concyclic
> 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.]
(Miquel cirle of the quadrilateral). Hence, this theorem is not a
Happy new year to all Hyacinthists. Jean-Pierre
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