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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
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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
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