+4609 200 points are equally spaced on the circumference of a circle. How many squares can be formed with 4 of the 200 points as vertices?
+36916 Each square requires 4 points.....then you can rotate it by 1 point....then 1 point again.....
you can rotate 49 times before you start to repeat the square pattern.....the original square plus 49 more = 50 squares.
+36916 Each square requires 4 points.....then you can rotate it by 1 point....then 1 point again.....
you can rotate 49 times before you start to repeat the square pattern.....the original square plus 49 more = 50 squares.
+4609 Solution
For any given one of the 200 points, we can find exactly one square with that point as one of the vertices---that point, the point diametrically opposite it, and the endpoints of the diameter that is perpendicular to the diameter formed by connecting the first two points. Each square then accounts for 4 vertices, so there are \(200/4=\boxed{50}\) squares.
