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arXiv · 2002.12777

Miquel-Steiner's point locus

Yuriy Zakharyan
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Abstract

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.

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Yuriy Zakharyan. 2020-02-26. Miquel-Steiner's point locus. https://arxiv.org/abs/2002.12777

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