梁绍鸿先生在其名著[1]中,介绍过一个颇为有趣的共圆点定理,即定理1设一圆与一三角形的外接圆同心且与各边(所在直线)相交,将各交点分别与对顶点相连,则诸连结线的中点共圆,这圆与三角形的九点圆同心.(三角形的九点圆,有人称它为欧拉圆,也有人称它为费尔巴哈圆.)[2]本文拟应用向量方法,将定理1类比推广到一般圆内接多边形中,导出两个更具普遍性的、面目有点出人意外的共圆点定理.为此,本文约定:(i)从n边形A1A2…An(≥3)的顶点集中任意除去一个顶点Aj(1≤j≤n),以其余n-1个顶点为顶点的n In his famous works [1], Mr. Liang Shaohong introduced a rather interesting co-ordinate theorem, namely, Theorem 1 sets a circle concentric with a circumscribed circle of a triangle and intersects with each edge (the line where it is located) When the vertices are connected, then the midpoints of the connecting lines are all round, which is concentric with the nine - point triangle of the triangle (nine o’clock of the triangle, some call it the Eulerian circle, and some call it the Feuerbach circle). [2] In this paper, we apply the vector method to generalize the theorem 1 to the general polygon, and derive two more common and somewhat unexpected co-ordinates theorems. ) Arbitrarily removes one vertex Aj (1 ≦ j ≦ n) from the vertexes of the n-polygons A1A2 ... An (≧ 3), n