  We study new types of geometric query problems defined as follows: given a
geometric set $P$, preprocess it such that given a query point $q$, the
location of the largest circle that does not contain any member of $P$, but
contains $q$ can be reported efficiently. The geometric sets we consider for
$P$ are boundaries of convex and simple polygons, and point sets. While we
primarily focus on circles as the desired shape, we also briefly discuss empty
rectangles in the context of point sets.
