The answer is infinite number of lines
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A line contains at least 2 points.
They define one plane. A line is defined by two points, and it takes three points to define a plane, so two points on the line, and one more point not on the line equals one plane.
many points, even curved line as long as the line is not broken it could go on for infinity!
There are one or infinitely many points.
Regardless of where you mark two points on a circle, there's only one possible line segment between them. It's called a "chord" of the circle.