关于多边形的顶点重心与圆内接多边形的垂心的若干结论

Some Results about Median Point of Any Polygon and Orthocenter of Any Inscribed Polygon of a Circle

利用递归方法给出任意多边形的中线与顶点重心的定义,再给出圆内接多边形高线的定义,然后证明圆内接多边形的高线(或所在直线)共点,由此得到圆内接多边形垂心的定义,最后给出多边形的顶点重心与圆内接多边形的垂心的若干性质。

In this article, we first give some definitions of central lines and median point of any polygon by recursion method, then give a definition of altitudes of a inscribed polygon of a circle. We also prove that the altitudes of a inscribed polygon of a circle are concurrent, then got a definition of orthocenter of a inscribed polygon of a circle. Finally give some properties of median point of any polygon and orthocenter of a inscribed polygon of a circle.