In Euclidian or plane geometry, there can be only one line through two fixed points. Lines cannot actually be drawn; if you see it it is not a geometric line. If the points are on a curved surface as in a geometry that is non-Euclidian, then there can be infinitely many lines connecting two points.
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In plane (Euclidian) geometry there is only one line through two points. On a sphere, every meridian intersects the north and south poles.
2 lines, I believe.
Infinite lines because a circle has infinite lines of symmetry.
A chord is a straight line drawn through a circle which divides the circle into two parts. The line can be drawn anywhere in the circle EXCEPT the center where it becomes the diameter.
exactly one