In the exercise answer on the basis of what appears to be true.

How many red points are 2 cm from point $O$?

The formation of circle is done by the set of points and each point has same distance from the point that is present at the center of the circle and the formation of a line is also done with the set of points.The distance between the points and the point in center of circle is the radius of circle.

The point $O$ represents the center of the circle and the distance of 1 cm represents the radius of the circle. The surface of the circle contains blue points which are infinite in count and the line that is travelling through the circle also contains the red points that are infinite in count.

As the formation of line is done with those red points which are infinite in count therefore the required count of points will the points that are having a distance of 2 cm from the point that is present at the center of the circle. So use a ruler and determine the count.

As the derived figure represents only 2 points on the horizontal line so the count of required point is 2.