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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

##### MSC:
 51N20 Euclidean analytic geometry 51M25 Length, area and volume in real or complex geometry
##### Keywords:
triangle; distance; extreme value; locus of expoints