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Expoints. (English) Zbl 0607.51013
Let \(\Delta\) be a triangle with vertices \(A_ 1\), \(A_ 2\), \(A_ 3\), and E a point in the plane. Denote by \(r_ i(E)\) the distance between E and \(r_ i\), and let m be a fixed real number. Then E is an expoint of \(\Delta\) if \(\sum^{3}_{i=1}r^ m_ i(E)\) has an extreme value at E.
The author observes that all expoints of \(\Delta\) are in \(\Delta\) and that the locus of expoints seems to consist of three branches, each of which connects a vertex and the midpoint of a side.
Reviewer: T.Bisztriczky

51N20 Euclidean analytic geometry
51M25 Length, area and volume in real or complex geometry