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Classical and weak lower bound for AP + BP + CP

Source: 5th German TST 2005, problem 3, not from the shortlist

May 12, 2005

geometryinequalitiesgeometry proposed

Problem Statement

Let

ABC

be a triangle with area

S

, and let

P

be a point in the plane. Prove that

AP+BP+CP\geq 2\sqrt[4]{3}\sqrt{S}