The Center and Radius of the Nine-Point Circle


	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, .


	Contributed by: Jay Warendorff

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

"The Center and Radius of the Nine-Point Circle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheCenterAndRadiusOfTheNinePointCircle/

Contributed by: Jay Warendorff

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Plane Geometry
Triangles

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A Collinearity between the Nine-Point Center, the Foot of an Altitude, and a Midpoint
Adams' Circle and the Gergonne Point
Nine-Point Circle
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A Triangle Formed by the Centers of Three Circles
Pairwise Tangent Circles Centered at the Vertices of a Triangle
The Fuhrmann Circle
The Nagel Point
The Hagge Circle

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