  It is shown that a construction of Z. Zhang and Y. Xiao on open subsets of
Ptolemaic spaces yields, when the subset has boundary containing at least two
points, metrics that are Gromov hyperbolic with parameter $\log 2$ and strongly
hyperbolic with parameter $1$ with no further conditions on the open set. A
class of examples is constructed on Hadamard manifolds showing these estimates
of the parameters are sharp.
