We examine a class of geometric theorems on cyclic 2n-gons. We prove that if we take n disjoint pairs of sides, each pair separated by an even number of polygon sides, then there is a linear combination of the angles between those sides which is constant. We present a formula for the linear combination, which provides a theorem statement in terms of those angles. We describe a program which uses this result to generate new geometry proof problems and their solutions.

翻译：我们研究了一类关于循环2n边形的几何定理。我们证明：若选取n对不相交的边，每对边之间相隔偶数条多边形边，则这些边之间夹角的线性组合为常数。我们给出了该线性组合的公式，从而得到关于这些夹角的定理陈述。描述了一个利用该结果生成几何证明新问题及其解答的程序。