# 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)