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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
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See theorem 209 in N. Altshiller-Court,
College Geometry
, Mineola, NY: Dover, 2007 p. 104.
RELATED LINKS
Circumcenter
(
Wolfram
MathWorld
)
Circumcircle
(
Wolfram
MathWorld
)
Circumradius
(
Wolfram
MathWorld
)
Euler Line
(
Wolfram
MathWorld
)
Nine-Point Circle
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
Nine-Point Circle
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
"
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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