  It is known that a simply connected Riemann surface satisfies the
isoperimetric equality if and only if it has constant Gaussian curvature. In
this article, we show that Randers Poincar\'e disc satisfies the isoperimetric
equality with respect to different volume forms. These metrics do not
necessarily have constant (negative) flag curvature. Thus we show that the
Osserman's result \cite{RO} in the Riemannian case can not be extended to the
corresponding Finslerian case.
