Problem 1651. Circumcircle Points

Determine the radius of the minimum sized circle that encompasses all the points.

Per Smallest Sphere Paper this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.

Input: Points (eg [0 0;0 1;2 0]) Minimum of 3 points

Output: r (radius of optimally centered circle)

Example: [0 0;0 1;2 0] yields [xc,yc,r] [1 .5 1.118] Output r=1.118

Theory: Best Circumcircle may occur in two ways:

1) Center of Line connecting pair with maximum separation, or

2) A circle utilizing three points from the set

Related Challenges:

Circle from 3 Points

Are Points in Circle

Warning: Rounding Errors may cause solution errors. Usage of 10*eps(r) may be appropriate.