Abstract
Properties of triangles such that the squares of their sides form an arithmetic progression were studied in 2018. In this paper, triangles with sides that form an arithmetic progression are described. Let a, b, c be sides of an arbitrary triangle ABC. If sides b, a, c of the triangle ABC form an arithmetic progression then, for example, the equality a=(b+c)/2 (b<a<c) holds. The class of triangles for which a=(b+c)/2 is greater than the class of triangles for which b, a, c form an arithmetic progression. In this paper, we study the properties of triangles for which this equality holds. Thus, triangles with sides that form an arithmetic progression are described with the help of the parameters p, R, r. Classes of rectangular triangles, triangles with angle 30°, triangles with angle 60°, triangles with angle 120° are studied and described.
Highlights
Let R and r be the circumradius and the inradius of an arbitrary triangle ABC
In [1], the authors studied properties of triangles such that the squares of its sides form an arithmetic progression. Description of such triangles associated with its remarkable points is given
The class of triangles for which a b+c 2 is greater than the class of triangles for which b, a, c form an arithmetic progression
Summary
ЛлMттааaййltссsккeииv,ййAгг.ооSсс.ууMддааoррnссaттвsвtееyннrннeыыvaйй педагогический университет (Барнаул, университет (Барнаул, Россия) Yu.12NАА. ллMттааaййltссsккeииv,ййAгг.ооSсс.ууMддааoррnссaттвsвtееyннrннeыыvaйй педагогический университет (Барнаул, университет (Барнаул, Россия)
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