Difference between revisions of "Nine point circle"
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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 
.
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