To determine whether the given statement is true or false, we need to recall the definition of a circle in geometry.
A circle is defined as the set of all points in a plane that are equidistant from a specific point. This specific point is called the center of the circle, and the constant distance from the center to any point on the circle is called the radius.
Let's break this down:
1. Center and Points on the Circle:
- Consider a fixed point in a plane, which we call the center.
- If we take several points that are the same distance from this center point, these points will lie on the circumference of a circle.
2. Equidistant Property:
- The defining property of a circle is that the distance from the center to any point on the circle (the radius) is always the same.
Given the definition and the properties of a circle as outlined above, the statement:
"A circle is the collection of points in a plane that are the same distance from a given point in the plane."
is indeed consistent with the definition of a circle. Therefore, the correct answer is:
A. True.
