It's a line... on a sphere...
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Two points. These may coincide if the line is a tangent to the 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.
Not necessarily. A plane dissecting a sphere would create a circle in that plane. so in order for the "line" to be both on the plane and the sphere the line would have to be a curve or segment of a circle.
Tangent
Diameter