Let's go through each option step-by-step to determine which statement best defines a circle.
### Option A:
"The set of all points in a plane that are the same distance from each other surrounding a given point called the center."
- This description is not correct because points on a circle are the same distance from a single given point (the center) rather than from "each other". Therefore, this statement is inaccurate.
### Option B:
"The set of all points in a plane that are the same distance from a given point called the center."
- This is a proper mathematical definition of a circle. It correctly states that a circle is formed by points that are equidistant from a given point, which is known as the center.
### Option C:
"Points in a plane that surround a given point called the center."
- This statement is incomplete and vague. It doesn't specify that the points are at a constant distance from the center, which is a crucial part of the definition of a circle.
### Option D:
"The set of all points that are the same distance from a given point called the center."
- This statement is almost correct, but it misses specifying that these points are in a plane. While a circle is indeed a set of points equidistant from a center, specifying the plane is essential for the definition.
Given these considerations, the statement that best defines a circle is:
[tex]\[ \boxed{B} \][/tex]
