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

Hyperbolic metrics on open subsests of Ptolemaic spaces with sharp parameter bounds