  A new similarity invariant metric $v_G$ is introduced. The visual angle
metric $v_G$ is defined on a domain $G\subsetneq\Rn$ whose boundary is not a
proper subset of a line. We find sharp bounds for $v_G$ in terms of the
hyperbolic metric in the particular case when the domain is either the unit
ball $\Bn$ or the upper half space $\Hn$. We also obtain the sharp Lipschitz
constant for a M\"obius transformation $f: G\rightarrow G'$ between domains $G$
and $G'$ in $\Rn$ with respect to the metrics $v_G$ and $v_{G'}$. For instance,
in the case $G=G'=\Bn$ the result is sharp.
