Given a sphere centered at the origin, with radius R, I want to find a point on the sphere such that the tangent to the sphere at that point divides the plane into 2 half spaces, such that the half-space NOT containing the sphere contains minimum number of points in a particular set.
Example: Sphere has radius 1. Set has 2 points that are diametrically opposite. In such a case, I can always choose a point on the sphere such that the tangent at the point divides the half space into 2 parts, and the one without the sphere has none of the 2 points in the set. I wish to extend this for further more points given in the set.
My attempt: Consider projections of points on the sphere, and their diameterically opposite points. Consider the tangents at all these points and then check which is the optimum point, however this fails for the simple case for 2 diameterically opposite points.