Tangent
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Two points. These may coincide if the line is a tangent to the sphere.
A Vertex is the point of intersection, and a Perpendicular Vertex is a vertex with all 90 degree angles, to be specific.
a line
It's a line... on a sphere...
a bisecting line ? Diameter ______________ The question needs to be re-thought. Lines do not cut spheres in half, no matter where the line is in the sphere. The simplest thing that can cut a sphere in half would be a plane.