Given point in space \(\displaystyle P(x_0 , y_0 , z_0 )\) , find the minimal distance between point and sphere: \(\displaystyle (x - a)^2 + (y - b)^2 + (z - c)^2 = r^2\).

The minimal distance between point and sphere lies on a line which passes through the center of the circle. So, find the length of the segment PC (C is the center of the sphere), then subtract r.