10900
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Excentral Triangle and a Related Hexagon
Let ABC be a triangle with excenters A', B', and C' opposite A, B, and C, respectively. Let A'', B'', and C'' be the circumcenters of A'BC, B'CA, and C'AB, respectively. Let
be the area of A'B'C' and
be the area of the hexagon AB''CA''BC''. Then
.
Contributed by:
Jay Warendorff
After work by:
Mehmet Sahin
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
See problem J95 in "Problem Column,"
Mathematical Reflections
[online], 4, 2008 p. 1.
RELATED LINKS
Circumcircle
(
Wolfram
MathWorld
)
Excenter
(
Wolfram
MathWorld
)
Excentral Triangle
(
Wolfram
MathWorld
)
Excircles
(
Wolfram
MathWorld
)
Hexagon
(
Wolfram
MathWorld
)
Polygon Area
(
Wolfram
MathWorld
)
PERMANENT CITATION
Jay Warendorff
"
The Excentral Triangle and a Related Hexagon
"
http://demonstrations.wolfram.com/TheExcentralTriangleAndARelatedHexagon/
Wolfram Demonstrations Project
Published: August 15, 2008
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
Area of a Hexagon Formed by the Vertices and Altitude Extensions of a Triangle
Jay Warendorff
Equilateral Triangles That Form a Star
Rik Agosti
Total Areas of Alternating Subtriangles in a 2n-gon
Jay Warendorff
Signed Area of a Polygon
Bruce Atwood (Beloit College) and Stan Wagon (Macalester College)
The Area of the Excentral Triangle
Jay Warendorff
Relations between Some Triangles Associated with Excircles
Jay Warendorff
Another Relation between the Areas of Triangles Associated with an Excircle
Jay Warendorff
A Relation between the Areas of Four Triangles
Jay Warendorff
The Area of the Contact Triangle
Jay Warendorff
Largest Isosceles Triangle Inscribed in a Circle
Jay Warendorff
Related Topics
Area
Plane Geometry
Polygons
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+