find a point such that the maximum distance to any point in a set of points P is minimized

Question

Given a set of points in 2d-space P, where Pi = (Xi, Yi),

I need to find a target point T such that the maximum distance to any Pi is minimized.

T does not need to exist in P, and can be defined arbitrarily

Is there an algorithm I can use for this?

Answer 1

This is the smallest circle problem.

Answer 2

http://www.cs.mcgill.ca/~cs507/projects/1998/jacob/problem.html

Think this may be a solution to your problem with pretty good explanation, but it's O(n^2)