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Barrow's inequality

 
Wikipedia: Barrow's inequality

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).\,

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