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

Triangle ABC with the nine point circle in light orange

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:

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 $N$.

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