The Product of the Inradius and Three Exradii
The Product of the Inradius and Three Exradii
Let ABC be a triangle with area and let be its inradius. Let , , and be the exradii of the excircles opposite A, B, and C, respectively. Then .
T
r
r
A
r
B
r
C
r=
r
A
r
B
r
C
2
T