  Recently a sequence of inequalities relating the black hole horizon, photon
sphere, shadow were proposed for spherically symmetric and static black holes,
providing the upper bound for given mass. In this paper, we extend the
discussion to include rotating black holes. When viewed from the north pole
direction, the shadow remains a round disk, but the image is skewed when viewed
from the equatorial plane. After properly implementing the ``size'' parameters
for the rotating black holes, we verify that the sequence of inequalities
remain valid for a variety of solutions, including Kerr, Kerr-Newman, Kerr-Sen
and Kerr-Cveti\v c-Youm black holes. The upshot is that rotation makes both the
actual and apparent sizes of a black hole smaller.
