When you try to draw a star, one way to begin is to join the first dot to the third dot i.e. miss out one dot each time as you go around. Why can't you draw a 6-pointed star in this way?
Now think about another way to draw the star. Does this work for a 6-pointed star?
Try to apply this to stars with more points and you should see the pattern!
If you go to the Printable Resources page, you can open and print PDF files of the circles (Circle templates > Without central point).