米克尔-斯坦纳点轨迹

摘要：

本文重新表述了Miquel-Steiner定理，并得到了任意三角形的Miquel-Steiner点轨迹。证明了该轨迹与共轭圆和Brocard圆有关。此外，我们还得到了当cevian相互垂直时，当cevian形成相似三角形时的Miquel-Steiner点轨迹.证明了如果Miquel-Steiner点属于直线，则Cevinans交点属于平行于等角的直线。最后，我们得到了一些结果的情况下，当Miquel-Steiner的点与三角形中心重合。

英文摘要：

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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