11453
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
A Triangle Formed by the Centers of Three Nine-Point Circles
Jay Warendorff
A Collinearity between the Nine-Point Center, the Foot of an Altitude, and a Midpoint
Jay Warendorff
Adams' Circle and the Gergonne Point
Jay Warendorff
The Triangle Formed by the Centers of the Miquel Circles
Jay Warendorff
A Triangle Formed by the Centers of Three Circles
Jay Warendorff
Pairwise Tangent Circles Centered at the Vertices of a Triangle
Jay Warendorff
The Fuhrmann Circle
Jay Warendorff
The Hagge Circle
Jay Warendorff
Another Concurrency Generated by Circles about a Triangle's Sides and Lines through an Internal Point
Jay Warendorff
A Concurrency Generated by Circles about a Triangle's Sides and Lines through an Internal Point
Jay Warendorff
Related Topics
Plane Geometry
Triangles
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+