# Feuerbach's Theorem

Jump to navigation
Jump to search

## 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 $\triangle ABC$.

## 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

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $9$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $9$ - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Feuerbach's Theorem** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**nine-point circle**