What is the definition of a circle? A circle is a plane figure with no straight sides. A circle is a point and all the points in a plane that are the same distance from it. A circle is the set of all points in a plane that are a given distance from a given line segment. A circle is the set of all points in a plane that are the same distance from a fixed point called the center.

Lets rule some out off the bat, shall we?
The first one you mentioned, a circle is a plane figure with no straight sides... I can name another shape with no straight sides... an oval.
The second one you mentioned, is a true statement
The third one you mentioned, a circle is from a point, not a line segment.
The last one mentioned is also a true statement.