  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.
