# Nine-point circle

From Citizendium

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In triangle geometry, the **nine-point circle** is a circle containing nine points of significance to the triangle: the mid-points of the sides; the feet of the altitudes; the mid-points of the segments from the vertices to the orthocentre. The centre of the nine-point circle lies on the Euler line; the radius is half that of the circumcircle.

## References

- H.S.M. Coxeter; S.L. Greitzer (1967).
*Geometry revisited*. MAA. ISBN 0-88385-619-0.