A Short Proof of a Ptolemy-Like Relation for an Even number of Points on a Circle Discovered by Jane McDougall

We give a short proof of a Ptolemy-style result first discovered and proved by Jane McDougall. It may be viewed as a generalization to any even number of points of the cubic relation connecting the six joint distances of four points on a circle (whose quadratic relation is the famed Plucker relation, alias Ptolemy's theorem). This article is in fond memory of Andrei Zelevinsky (1953-2013) who loved Ptolemy's theorem.