Answer :
Let's analyze each option to understand which best defines a circle.
A. The set of all points in a plane that are the same distance from a given point called the center.
- This statement correctly and clearly describes a circle. A circle is indeed all points that are equidistant from a central point.
B. The set of all points that are the same distance from a given point called the center.
- This statement is close but lacks one important element: it does not specify that the points need to lie in a plane. Without this clarification, the definition is incomplete, as points at the same distance from a central point can form a sphere in three-dimensional space.
C. OD.
- There appears to be a formatting error here, making this option invalid for consideration.
D. The set of all points in a plane that are the same distance from each other surrounding a given point called the center.
- This statement is incorrect. A set of points that are the same distance from each other would describe a different geometric concept. The correct definition should focus on all points being equidistant from a single central point, not from each other.
Given this analysis, the best definition of a circle is provided by:
A. The set of all points in a plane that are the same distance from a given point called the center.
A. The set of all points in a plane that are the same distance from a given point called the center.
- This statement correctly and clearly describes a circle. A circle is indeed all points that are equidistant from a central point.
B. The set of all points that are the same distance from a given point called the center.
- This statement is close but lacks one important element: it does not specify that the points need to lie in a plane. Without this clarification, the definition is incomplete, as points at the same distance from a central point can form a sphere in three-dimensional space.
C. OD.
- There appears to be a formatting error here, making this option invalid for consideration.
D. The set of all points in a plane that are the same distance from each other surrounding a given point called the center.
- This statement is incorrect. A set of points that are the same distance from each other would describe a different geometric concept. The correct definition should focus on all points being equidistant from a single central point, not from each other.
Given this analysis, the best definition of a circle is provided by:
A. The set of all points in a plane that are the same distance from a given point called the center.
