Dr. H. Vogel - Zentrum Mathematik - Technische Universität München

NINE-POINT-CIRCLE

The NINE-POINT-CIRCLE of a triangle ABC (discovered by FEUERBACH) contains the:

  • three vertices Fa, Fb, Fc of the orthoptic triangle of the triangle ABC,
  • three midpoints Ma, Mb, Mc of the sides of the triangle ABC,
  • three midpoints Na, Nb, Nc of the line segment from the orthocentre H to the vertices A, B, C of the triangle ABC,
The centre N of the NINE-POINT-CIRCLE lies on the EULER-LINE [HSMu] of the triangle ABC with the median point S and bisects the line segment from the orthocentre H to the circumcentre Mu.

Bitte schalten Sie Java ein, um eine Cinderella-Konstruktion zu sehen.
You can move the points A, B, C by mouse-clicking.

One can find a nice elementary proof of the NINE-POINT-CIRCLE in "Excursions in Geometry" by C. S. OGILVY, Oxford University Press, NY. Karl Wilhelm FEUERBACH (1800 - 1834) was a teacher of maths at the high school at Erlangen.

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I'm waiting for your remarks using E-mail: vogel@mathematik.tu-muenchen.de !
Dr. H. Vogel , Zentrum Mathematik der Technischen Universität München ,