Nine-point circle

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.