Hellenica World

# .

In geometry, Barrow's inequality states the following: Let P be a point inside the triangle ABC; U, V, and W be the points where the angle bisectors of BPC, CPA, and APB intersect the sides BC, CA, AB, respectively. Then

$$PA+PB+PC\geq 2(PU+PV+PW).\,$$

Barrow's inequality strengthens the Erdős–Mordell inequality, which has a similar form with PU, PV, and PW replaced by the three distances of P from the triangle's sides. It is named after David Francis Barrow.