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The Area of the Incentral Triangle
Let ABC be a triangle and let the bisectors of the angles at A, B, C meet the opposite sides at A', B', C'. Let
be the area of ABC and
be the area of A'B'C'. Let
,
and
be the lengths of BC, CA, and AB, respectively. Then
.
Contributed by:
Jay Warendorff
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See problem 4.69 in V. Prasolov,
Problems in Plane and Solid Geometry
, Vol. 1,
Plane Geometry
[PDF], (D. Leites, ed. and trans.).
RELATED LINKS
Angle Bisector
(
Wolfram
MathWorld
)
Incentral Triangle
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
The Area of the Incentral Triangle
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheAreaOfTheIncentralTriangle/
Contributed by:
Jay Warendorff
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