Definition:Feuerbach Circle

Definition
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 $\triangle ABC$.


 * 9PointCircle.png

Also see

 * Nine Point Circle Theorem
 * Feuerbach's Theorem