To determine which description defines a circle, let's evaluate each option provided in the question:
1. Two rays with a common endpoint: This describes an angle, not a circle. An angle is formed by two rays (or line segments) that share the same endpoint, known as the vertex.
2. A piece of a line with two endpoints: This describes a line segment. A line segment is a part of a line that is bounded by two distinct endpoints.
3. A piece of a line with one endpoint: This describes a ray. A ray starts at one point (the endpoint) and extends infinitely in one direction.
4. All coplanar points equidistant from a given point: This is the definition of a circle. A circle is the set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center).
By analyzing each option, we can see that the correct definition of a circle is:
All coplanar points equidistant from a given point.
Thus, the correct answer is:
Option 4 - All coplanar points equidistant from a given point.
