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Functional equations associated with triangle geometry. (English) Zbl 0774.39006
The author investigates triangle geometry in the context of functional equations of three variables \(a\), \(b\), \(c\), being the sidelengths of a variable triangle. Triangle centres (e.g. incenter, circumcenter, centroid) and central lines (e.g. Euler line) are defined and partitioned into six classes. Criteria for some geometric relations (e.g. parallelism, perpendicularity) are given in terms of these classes.

MSC:
39B22 Functional equations for real functions
51N20 Euclidean analytic geometry
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References:
[1] Carr, G. S.,Formulas and theorems in Pure Mathematics, 2nd ed., Chelsea, New York, 1970. · Zbl 0209.00102
[2] Eves, H. andKimberling, C. H.,Isogonal and isotomic conjugates. Amer. Math. Monthly93 (1986), 132–133. · doi:10.2307/2322716
[3] Kimberling, C. H.,Central points and central lines in the plane of a triangle, to appear in Math. Magazine. · Zbl 0821.51014
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