10753
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Sum of the Squares of the Distances from the Vertices to the Orthocenter
Let ABC be a triangle with orthocenter H and let
be the circumradius of ABC. Then:
AH
^{2}
+BH
^{2}
+CH
^{2}
=12
R
^{2}
-(AB
^{2}
+BC
^{2}
+AC
^{2}
)
Contributed by:
Jay Warendorff
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
See Theorem 204 in N. Altshiller-Court,
College Geometry
, 2nd ed., Mineola, NY: Dover, 2007 p. 102.
RELATED LINKS
Circumradius
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
The Sum of the Squares of the Distances from the Vertices to the Orthocenter
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheSumOfTheSquaresOfTheDistancesFromTheVerticesToTheOrthocen/
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
The Sum of the Distances from the Orthocenter to the Vertices
Jay Warendorff
The Distance to the Orthocenter from a Vertex
Jay Warendorff
The Distance to the Orthocenter
Jay Warendorff
The Product of the Distances of the Incenter to the Vertices
Jay Warendorff
The Circumcircle of the Orthocenter and Two Vertices and a Parallelogram
Jay Warendorff
The Distances to the Incenter and Excenters from the Circumcenter
Jay Warendorff
The Distance from the Circumcenter to an Excenter
Jay Warendorff
Circles through the Orthocenter
Jay Warendorff
Projections, an Altitude, and the Orthocenter
Jay Warendorff
The Orthocenter of the Medial Triangle
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+