arXiv subjects

Yuriy Zakharyan

Publications and source records attributed to Yuriy Zakharyan.

2 recordsLinked to original sources

arXiv2020

Varignon's and Wittenbauer's parallelograms

In this paper the concept of homothetic parallelogram is introduced. This concept is a generalization of Varignon's and Wittenbauer's parallelograms of an arbitrary quadrangle, whose diagonals are not parallel. A formula for the area and perimeter of a homothetic parallelogram for the case when quadrangles are not crossed is obtained. The fact that homothetic parallelograms are similar to one another and are in perspective from diagonals intersection point is proved.

math.HO↗

arXiv2020

Miquel-Steiner's point locus

In this paper we reformulate Miquel-Steiner's theorem and we obtain Miquel-Steiner's point locus for an arbitrary triangle. We prove that this locus is related to conjugate circles and Brocard's circle. In addition, we obtain Miquel-Steiner's point locus in a case when cevians are perpendicular to each other, in a case when cevians form similar triangles. In addition, we prove that if Miquel-Steiner's point belongs to line, then cevinans intersection point belongs to line which is parallel to isogonal. Finally, we obtain few result for cases when Miquel-Steiner's point coincides with triangle centres.

math.HO↗