To understand whether the given statement is true or false, let's analyze the definition of a circle.
A circle is a fundamental concept in geometry. The definition of a circle can be stated as follows:
A circle is the set of all points in a plane that are at a fixed distance from a given point. This fixed distance is called the radius of the circle, and the given point is called the center of the circle.
Thus, if we break down the statement provided:
- "A circle is the collection of points in a plane..." - This is correct because a circle, by definition, consists of all points that meet a certain condition in a two-dimensional plane.
- "... that are the same distance from a given point in the plane." - This is also correct because the defining feature of a circle is that all points on the circle are equidistant from the center.
Given our analysis, we can determine that the statement provided is a true definition of a circle in geometry.
Therefore, the correct answer is:
A. True
