  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.
