A circle has infinitely many points of symmetry. Every straight line that passes through the center of a circle is a line of symmetry.
Only one line can be drawn through eight points.
An infinite number of lines can be drawn through a single point, but only one through two points (of course, if the points don't have the same coordinates).
Since the question does not require them to be straight lines, the answer is infinitely many.
If you're talking about straight lines (not curves) the answer is one.
It has 8. Each passes through the centre. Four pass through vertices, four pass through the mid-points of opposite sides. 4
It has 8. Each passes through the centre. Four pass through vertices, four pass through the mid-points of opposite sides
It has 8. Each passes through the centre. Four pass through vertices, four pass through the mid-points of opposite sides
It has 8. Each passes through the centre. Four pass through vertices, four pass through the mid-points of opposite sides.
A circle has infinitely many points of symmetry. Every straight line that passes through the center of a circle is a line of symmetry.
9
one
1
Only one line can be drawn through eight points.
There are 66 lines. As no 3 points are co-linear, every line passes through exactly two of the points. Thus every point is joined by one of the lines to every other point. So it looks like there are 12 × 11 = 132 lines. However, the line joining point A to point B is the same as the line joining point B to point A; in other words, every line has been counted twice, once for one of the points it passes through and again by the other point it passes through. Therefore there are half the number of lines discovered above, name 132 ÷ 2 = 66 lines. This is the same as the "handshake problem" where everyone at a party shakes hands with everyone else at the party and the question is how many handshakes are there; the points are the people and the lines are the handshakes.
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.
An infinite number of lines can be drawn through a single point, but only one through two points (of course, if the points don't have the same coordinates).