# Difference between revisions of "Nine point circle"

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+ | [[Image:Euler Line.PNG|thumb|500px|right|Triangle ''ABC'' with the nine point circle in light orange]] | ||

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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 '''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 [[altitude]]s of the triangle. | * The three feet of the [[altitude]]s of the triangle. |

## Revision as of 14:47, 26 September 2007

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.*