circle
A circle or a sphere would fit the given description.
The apothem is the distance from the center to the middle of any side on a regular polygon. That is, a shape with every single side and angle the same.
A circle is the set of all the points that are the same (arbitrary) distance (called the radius) from some (arbitrary) point (called the center).
line
A sphere.
If the shape is two-dimensional then it is a circle, if the shape is three-dimensional then it's a sphere.
A circle or a sphere could fit the given description
The shape of a circle is round. Circles are plane shapes that have all points that are the same distance from the center.
A circle has all of it's points the same distance from the center. For example, if you put a dot on a given point on the circumference, or outline of a circle, all the points have the same distance from the circle. This only works if you put a point on the outline or circumference of the circle.
circle, square, equilateral triangle, rhombus, etc.
A circle is the set of all the points that have the same distance from a given point (its center). If you rotate a shape, you rotate it in such a way that you keep any point a fixed distance from the center of rotation.
A curved surface on which all points are the same distance from the center is called a sphere.
In 2 dimensions, it's a circle. In 3 dimensions, it's a sphere.
A circle is a set of points equidistant ( the same distance ) away from a single point, the center of the circle.
if it's a circle, all points are equidistant from the center.
A circle.