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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:
| + | #REDIRECT[[Nine-point circle]] |
| − | * The three feet of the [[altitude]]s of the triangle.
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| − | * The three [[midpoint]]s of the [[edge]]s of the triangle.
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| − | * 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.)
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| − | That such a circle exists is a non-trivial theorem of [[Euclidean geometry]].
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| − | The center of the nine point circle is the [[nine-point center]] and is usually denoted <math>N</math>.
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| − | {{stub}}
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| − | {{definition}}
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