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Feuerbach's theorem

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Feuerbach's theorem

the theorem that the nine-point circle of any triangle is tangent to the incircle and to the three excircles

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About Feuerbach's theorem

In the geometry of triangles, the incircle and nine-point circle of a non-equilateral triangle are internally tangent to each other at the Feuerbach point of the triangle. The Feuerbach point is a triangle center, meaning that its definition does not depend on the placement and scale of the triangle. It is listed as X(11) in Clark Kimberling's Encyclopedia of Triangle Centers, and is named after Karl Wilhelm Feuerbach.

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Facts from Wikidata (CC0).