Given a set of N points in general position on the plane, give efficient algorithms to find

1. the smallest semicircular region (semidisk) that contains the points
2. the smallest circular segment that contains the points (2 variants - 'smallest' could mean either of 'least area' or 'least perimeter'). 
3. the smallest sector that contains the points (again, 2 variants)

I am not aware of previous works on these questions.