Let's consider the definition of a circle.
A circle can be defined geometrically as follows:
1. It is a set of all points in a plane that are at a constant distance from a fixed point. This fixed point is known as the center of the circle, and the constant distance is called the radius of the circle.
Now let's analyze the given options one by one:
1. Two rays with a common endpoint: This forms an angle, not a circle. It isn't related to the properties of a circle.
2. A piece of a line with two endpoints: This describes a line segment. A line segment does not meet the definition of a circle as it does not involve a set of points equidistant from a fixed point.
3. A piece of a line with one endpoint: This describes a ray, which is a straight path extending infinitely in one direction from a single point. Again, this does not correspond to a circle.
4. All coplanar points equidistant from a given point: This is the correct geometrical definition of a circle. Any point that is a constant distance (radius) from a central point (center) in the same plane forms a circle.
Therefore, the correct answer is:
All coplanar points equidistant from a given point.
