The Area of the Incentral Triangle
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 .
S
S'
a
b,
c
S'=S
2abc
(a+b)(b+c)(c+a)