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.