how to find the minimum covering radius for a set of scattered points

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I might show my stupidity here but are you sure about this:

I may be stupid too but don't you just have to first find the bounding rectangle (the smallest rectangle that contains all points)? The diagonal of this rectangle will be the diameter of the smallest covering circle.

To find the bounding rectangle is easy. Just find the minimum and maximum x and y coordinates. The diagonal is then the line from (x_min, y_min) to (x_max, y_max). The length of this line is sqrt((y_max - y_min)^2 + (x_max - x_min)^2). This is also the diameter of the covering circle. Half it and you get the radius.

The centre of the covering circle is placed in the middle of the bounding rectangle which is the mid-point of the diagonal line calculated above.