The correct definition of a circle is:
A set of all points in a plane that are the same distance from a given point.
To explain step-by-step why this definition is correct:
1. Definition Analysis:
- A circle is a geometric shape.
- To be classified as a circle, every point on its boundary (circumference) must be equidistant from a central point (called the center).
2. Examination of Given Options:
- Option 1: "A closed figure with three or more straight sides" - This is the definition of a polygon, not a circle.
- Option 2: "A polygon with all sides of equal length" - This defines a regular polygon where all sides and angles are equal, such as an equilateral triangle or a square, but not a circle.
- Option 3: "A set of all points in a plane that are the same distance from a given point" - This precisely describes a circle, where the given point is the center and the equal distance is the radius.
- Option 4: "A line segment connecting two points on a curve" - This is the definition of a chord, not a circle.
3. Conclusion:
By evaluating each option, it is clear that only "a set of all points in a plane that are the same distance from a given point" accurately describes what a circle is. Therefore, this definition is correct.
