Nine point circle

The nine point circle (also known as Euler's circle or Feuerbach's circle) of a given triangle is a circle which passes through 9 "significant" points:

 * The three feet of the altitudes of the triangle.
 * The three midpoints of the edges of the triangle.
 * The three midpoints of the segments joining the  vertices of the triangle to its orthocenter.  (These points are sometimes known as the Euler points of the triangle.)

That such a circle exists is a non-trivial theorem of Euclidean geometry.

The center of the nine point circle is the nine-point center and is usually denoted .

This article is a stub. Help us out by expanding it. Template:Definition