Feuerbach's Theorem

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Theorem

Let $\triangle ABC$ be a triangle.

The Feuerbach circle of $\triangle ABC$ is tangent to:

the incircle of $\triangle ABC$

and:

the $3$ excircles of $\triangle ABC$.


9PointCircleTangentCircles.png


Proof


Also see


Source of Name

This entry was named for Karl Wilhelm Feuerbach.


Historical Note

Feuerbach's Theorem was proved in $1822$ by Karl Wilhelm Feuerbach.

This was two years after Jean-Victor Poncelet and Charles Julien Brianchon had demonstrated the existence of the nine point circle, now known as the Feuerbach circle.


Sources