Question

What is the definition of a circle?

Answer 1

Let's go through each answer and see what shape it describes.

"A circle is the set of all points in a plane that are the same distance from a fixed point on another plane"

The shape these conditions form is dependent on where on the plane the fixed point is, and how one plane is oriented in relation to the other. So, these conditions can but don't necessarily make a circle.

"A circle is a closed plane figure with no straight sides"

Circles are closed and don't have straight sides, but ellipses also meet these conditions.

"A circle is the set of all points in a plane that are the same distance from a fixed point called the center"

Imagine an arm that is attached to a hinge. Move that arm around the hinge. What shape does the point on the end of the arm form? A circle. The location of the hinge is the center and the length of the arm is the radius.

"A circle is the set of all points that are a given distance from a given line."

These conditions don't limit the resulting shape to a plane, so the shape would be three dimensional.

So the correct answer is the third answer.