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Welcome to Feuerbach Theorem, one of the most striking theorems in triangle geometry!
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Feuerbach Theorem: Table of Content




Feuerbach Point Facts


Feuerbach Theorem, Acute Triangle illustration


Feuerbach Theorem, Obtuse Triangle illustration


Feuerbach Theorem, Right Triangle illustration


Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.


Spieker Center


Symmedian (Lemoine) Point


Steiner Point


Mittenpunkt Point

Karl Feuerbach (1800-1834) was a geometer who discovered the nine-point circle of a triangle.

One of the most striking theorems in triangle geometry is Feuerbach's theorem. He wrote in his 1822 paper:

The circle which passes through the feet of the altitudes of a triangle touches all four of the circles which are tangent to the three sides of the triangle; it is internally tangent to the inscribed circle and externally tangent to each of the circles which touch the sides of the triangle externally.

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Last updated: May 25, 2008