关于圆的一个定值问题的推广

An Expansion of the Constant Problem of a Circle

设P是圆上任意一点 ,P到与圆外离 (内离、相交 )正n边形A1A2 …An 各边的距离分别为d1,d2 ,… ,dn,本文给出当m为自然数时 ,∑ni =1dmi 为定值的条件以及 ∑ni =1dmi 为定值时的定值表达式。

Given that \$P\$ is an arbitrary point in a circle,let \$d\-1,d\-2,\:d\-n\$ be respectively distances from \$P\$ to each side of equilateral n-polygons out-chordless/in-chordless/intersecting with the circle.This paper gives an condition for \$∑ni=1d\+m\-i\$ being a constant when \$m\$ is a natural number,and establishes the formula of \$∑ni=1d\+m\-i\$ when \$∑ni=1d\+m\-i\$ is constant.