Circular separability of polygons

Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A li near-time algorithm is proposed to decide if two polygons are circularly se parable. The algorithm outputs the smallest separating circle. The second p roblem asks for the largest circle included in a preprocessed, convex polyg on, under some point and/or line constraints. The resulting circle must con tain the query points and it must lie in the halfplanes delimited by the qu ery lines.