Forum Geometricorum, 1 (2001) 75 -- 79.
Abstract: An effective method for the proof of geometric inequalities is the use of the dot product of vectors. In this paper we use this method to solve some famous problems, namely Heron's problem, Fermat's problem and the extension of the previous problem in space, the so called Gergonne's problem. The solution of this last is erroneously stated, but not proved, in F.G.-M.
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