North pole of the sphere must be vertical to the plane. And the line touching only the north pole would be tangent to the circle, and this tangent would be perpendicular to the radius of the sphere touching that point (North Pole) , which means the line touching the north pole only would be parallel to the plane (I mean to the line on the plane vertically below it) and the distance of it from the plane would be equal to the radius, always. So unless the radius of the sphere is equal to 0, or the plane is not flat, the line will never touch the plane, which means there is no point 'infinity' on the plane! Or is it that, that very thing is called infinity? I mean, is the point that never comes infinity?? Or am I wrong?? Is the actual matter quite different????????? Please help....