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The Area of the Incentral Triangle

​
a
≈
5.57
b
≈
3.78
c
≈
5.64
S
≈
9.96
2abc
(a+b)(a+c)(b+c)
S
≈
2.40
S'
≈
2.40
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
S
be the area of ABC and
S'
be the area of A'B'C'. Let
a
,
b,
and
c
be the lengths of BC, CA, and AB, respectively. Then
S'=
2abc
(a+b)(b+c)(c+a)
S
.
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