\begin{definition}[Definition:Feuerbach Circle]
Let $\triangle ABC$ be a triangle.
The '''Feuerbach circle''' of $\triangle ABC$ is the circle which passes through each of the $9$ points:
: the feet of the altitudes of $\triangle ABC$
: the midpoints of the sides of $\triangle ABC$
: the midpoints of the lines from the vertices of $\triangle ABC$ to the orthocenter of $\triangle ABC$.
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\end{definition}