Nine point circle: Difference between revisions
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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 three feet of the [[altitude]]s of the triangle. | |||
* The three [[midpoint]]s of the [[edge]]s of the triangle. | |||
* The three midpoints of the segments joining the [[vertex | vertices]] of the triangle to its [[orthocenter]]. (These points are sometimes known as the [[Euler point]]s 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 <math>N</math>. | |||
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Revision as of 10:45, 6 July 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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