WOLFRAM|DEMONSTRATIONS PROJECT

The Product of the Distances of the Incenter to the Vertices

​
AI
≈
5.28
BI
≈
2.82
CI
≈
3.32
R
≈
4.00
r
≈
1.76
AI
×
BI
×
CI
≈
49.37
4
R
2
r
≈
49.37
Let ABC be a triangle and I the incenter. Let
R
be the circumradius and
r
the inradius. Then
AI×BI×CI=4R
2
r
.