On Hausdorff intrinsic metric

In this paper we prove that in the set of all nonempty bounded closed subsets of a metric space $(X,\rho)$ the Hausdorff metric is the Hausdorff intrinsic metric if and only if the metric $\rho$ is an intrinsic metric. In a space with an intrinsic metric we obtain the upper bound for the Hausdorff distance between generalized balls.