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A Generalization of Hansen's Theorem
Let ABC be a triangle and H its orthocenter. Let
and
R
be the radii of the incircle and circumcircle. Let
,
, and
be the radii of the excircles opposite A, B, and C. Then
.
Contributed by:
Jay Warendorff
After work by:
Amy Bell
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See
Hansen's Right Triangle Theorem, Its Converse and a Generalization.
RELATED LINKS
Excircles
(
Wolfram
MathWorld
)
Circumcircle
(
Wolfram
MathWorld
)
Incircle
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
A Generalization of Hansen's Theorem
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AGeneralizationOfHansensTheorem/
Contributed by:
Jay Warendorff
After work by:
Amy Bell
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