A Line Segment contain infinite points and Sinc you are talking about a side then we can treat the side as Line Segment.
If we take a regular n-sided polygon where n tends to infinity then sides or Line Segment will approaches to point but not exactly point and in that way the regular polygon approaches to circle but not exactly becomes the circle.
Note: In geometry , the line, point are undefined terms so we can't claim about the Number of sides of Circle.
You should note that Point is dimension less means it has no length, breadth ,height and it is infinitely small quantities and these infinite points makes line so if we choose any two points on line say A and B and claim that distance between A and B is infinitely small then can we say that single point will lies Between them? DEFINATELY NOT, because we can put more infinite small points between A and B.