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A circle does not have a set of parallel lines in the traditional sense, as parallel lines are defined as lines that never intersect and remain equidistant from each other. However, you can draw lines that are tangent to a circle at various points, and these tangent lines can be parallel if they are at the same distance from the center of the circle. But in the context of the circle itself, it does not contain parallel lines.
Parallel lines within a circle are infinite.
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A circle intersected by a pair of parallel lines.
They do not have any specific name.