  Delaunay triangulations of a point set in the Euclidean plane are ubiquitous
in a number of computational sciences, including computational geometry.
  Delaunay triangulations are not well defined as soon as 4 or more points are
concyclic but since it is not a generic situation, this difficulty is usually
handled by using a (symbolic or explicit) perturbation. As an alternative, we
propose to define a canonical triangulation for a set of concyclic points by
using a max-min angle characterization of Delaunay triangulations. This point
of view leads to a well defined and unique triangulation as long as there are
no symmetric quadruples of points. This unique triangulation can be computed in
quasi-linear time by a very simple algorithm.
