We study the problem of computing stabbing circles of a set S of n line segments in the plane. We provide
efficient algorithms: (i) to compute a representation of all the combinatorially different stabbing circles for
S, and the ones with maximum and minimum radius, in O(n^2) time and space; (ii) to decide if there exists
a stabbing circle for a set of parallel segments in O(n log^2 n) time and O(n) space.