  We prove a pair of sharp reverse isoperimetric inequalities for domains in
nonpositively curved surfaces: (1) metric disks centered at the vertex of a
Euclidean cone of angle at least $2\pi$ have minimal area among all
nonpositively curved disks of the same perimeter and the same total curvature;
(2) geodesic triangles in a Euclidean (resp. hyperbolic) cone of angle at least
$2\pi$ have minimal area among all nonpositively curved geodesic triangles
(resp. all geodesic triangles of curvature at most $-1$) with the same side
lengths and angles.
