Sawayama-Thébault's theorem

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Thébault's theorem: The centers of the three inner circles P, I and Q lie on a common (red) straight line

The set of Sawayama-Thébault or even set of Thébault (after Victor Thébault ) is a statement of elementary geometry on certain circles at any triangle .

In any triangle ABC connect any point M from the inside of the side BC with A. Then there are two circles, each touching the lines BC and AM as well as the circumference of the triangle ABC. The centers of these two circles and the center of the inscribed circle then lie on a common straight line .

literature

  • Jean-Louis Ayme: Sawayama and Thébault's Theorem . Forum Geometricorum, Volume 3, 2003, pp. 225-229.
  • Alexander Ostermann, Gerhard Wanner: Geometry by Its History . Springer, 2012, pp. 227-230

Web links