The sphere forms a circle in the plane.
There are two bits of sphere which are spherical caps with a circular base.
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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.
plane perras
great circle
plane shape
A sphere has an infinite number of planes of symmetry. The plane must include the center of the sphere, but it can tilt at any angle. The question is the same as asking "How many planes can be drawn through one point ?" The answer is: An infinite number. And as long as the point is the center of the sphere, each plane is a plane of symmetry of the sphere.