  We consider a projection from the center of the unit sphere to a tangent
space of it, the central projection, and study two area minimizing problems of
the image of a closed subset in the sphere. One of the problems is the
uniqueness of the tangent plane that minimizes the area for an arbitrary fixed
subset. The other is the shape of the subset that minimizes the minimum value
of the area. We also study the similar problems for the hyperbolic space.
