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Let ABC be a triangle with orthocenter H, circumcenter O, and circumradius

. Let the nine-point circle have center N and radius

Then N lies on OH (the Euler line) and bisects OH.

Also,

See theorem 209 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 104.

Contributed by: Jay Warendorff

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The Center and Radius of the Nine-Point Circle