本文应用Ptolemy定理,讨论正多边形外接圆周上任意一点到各顶点距离之间的关系。 Ptolemy定理圆内接四边形中两条对角线之积等于两双对边乘积之和(图1)。 AC·BD=AB·CD+AD·BC. 例1 两边三角形外接圆周上任意一点,到三顶点距离中,最长的一段等于其余两段之和(如图2)。证明因为四边形ABPC内接于圆,所 In this paper, the Ptolemy theorem is used to discuss the relationship between any point on the circumcircle of a regular polygon to the distance between each vertex. Ptolemy Theorem The product of two diagonals in a circle inscribed quadrilateral is equal to the sum of the products of two pairs of opposite edges (Figure 1). AC · BD = AB · CD + AD · BC. Example 1 Both sides of the triangle circumscribed any point, to the distance between the three vertices, the longest section is equal to the sum of the remaining two sections (Figure 2). It is proved that because the quadrilateral ABPC is inscribed in a circle,