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Feuerbach's Theorem: What Is It About?
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Copyright © 1996-2008 Alexander Bogomolny
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This is a famous result discovered by Karl Wilhelm Feuerbach (1800-1834): the 9-point circle of a triangle touches its incircle and the three excircles. Feuerbach proved the theorem by computing algebraically the distances between the centers of the circles. Other proofs depend on the inversion in a circle. The point of tangency of the incircle and the 9-point circle is known as the Feuerbach point. The 9-point circle is known to house a few dozen other intereseting points. The points of tangency in Feuerbach's theorem are involved in two cases of incidence.
Nine Point Circle
- Feuerbach's Theorem
- Feuerbach's Theorem
- Four Triangles, One Circle
- Hart Circle
- Feuerbach's Theorem
- Six Point Circle
- Nine Point Circle
- Inversion in the Incircle
Copyright © 1996-2008 Alexander Bogomolny
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