10527
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Area of the Excentral Triangle
Let
be the area of the triangle formed by the excenters of a triangle with perimeter
and circumradius
. Then
.
Contributed by:
Jay Warendorff
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
See Theorem 233 in N. Altshiller-Court,
College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle
, Mineola, NY: Dover, 2007 p. 113.
RELATED LINKS
Circumcircle
(
Wolfram
MathWorld
)
Circumradius
(
Wolfram
MathWorld
)
Excenter
(
Wolfram
MathWorld
)
Excentral Triangle
(
Wolfram
MathWorld
)
Excircles
(
Wolfram
MathWorld
)
Perimeter
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
The Area of the Excentral Triangle
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheAreaOfTheExcentralTriangle/
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 Excentral Triangle and a Related Hexagon
Jay Warendorff
The Area of the Contact Triangle
Jay Warendorff
The Area of a Triangle, its Circumradius, and the Perimeter of its Orthic Triangle
Jay Warendorff
The Area of the Pedal Triangle of the Centroid
Jay Warendorff
The Area of a Triangle as Half a Rectangle
Jay Warendorff
The Area of a Triangle inside the Incircle
Jay Warendorff
Area of a Hexagon Formed by the Vertices and Altitude Extensions of a Triangle
Jay Warendorff
Two Triangles of Equal Area on Either Side of an Angle Bisector
Jay Warendorff
Another Relation between the Areas of Triangles Associated with an Excircle
Jay Warendorff
On the Areas of Triangles Associated with an Excircle
Jay Warendorff
Related Topics
Area
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+