WOLFRAM|DEMONSTRATIONS PROJECT

Barrow's Inequality

​
PA
+
PB
+
PC
≈
25.97
2
(
PA'
+
PB'
+
PC'
)
≈
25.35
Let P be an internal point of the triangle ABC. Let the angle bisectors of the three angles from P to the vertices of ABC meet its sides at A', B', and C'.
Then
PA+PB+PC≥2(PA'+PB'+PC')
.