The shape you are describing is a circle. A circle is defined as the set of all points in a plane that are equidistant from a central point, known as the center. The curved side of a circle is its circumference, which is always the same distance (the radius) from the center.
That shape is called a circle.
Equilateral
Yes. In a perfect sphere the centre is an equal distance from any point from the surface.
If two chords are the same distance from the center of a circle, they are equal in length. This is due to the property of circles where equal distances from the center to the chords indicate that the chords lie parallel to each other and are congruent. Thus, the relationship between the center and the chords confirms their equality in length.
A spherical surface, with its center at the given point, and its radius equal to the given distance.
That shape is called a circle.
A plane mirror is not curved so it does not have a center of curvature. Or if you want to be mathematically correct, you could say that it's center of curvature is at an infinite distance from the mirror.
No, distance is not always greater than or equal to the magnitude of displacement. Distance measures the total path length traveled, while displacement is the straight-line distance between the initial and final positions. In some cases, especially with curved paths, the distance can be greater than the displacement.
a circle
Equilateral
Yes. In a perfect sphere the centre is an equal distance from any point from the surface.
A sphere
a sphere
vertices
Yes, that is correct
They are congruent They are equidistant from the center of the circle.
The distance from the center of a mirror to the focal point is equal to the focal length of the mirror. This distance is half the radius of curvature of the mirror.