The definition of a circle uses the undefined term _______.

The definition of a circle uses the undefined term _______.

A. arc

B. line

C. plane

D. ray

Answer: B. line

Using the joined-up dots the definition of a circle used the undefined term line in the context of points and distance from a point. A circle is the collection of all points located on a plane such that the distance of all these points from a fixed point known as the centre is the same and is termed as radius. This fixed distance is measured on a straight line from the centre to any point on the circle and this is where the undefined term ‘line’ is used.

You might define specific concepts as ‘undefined’ in the context of geometry because if complex concepts are broken down too much, they are defined in terms of these ‘undefined’ concepts. In most cases “point,” “line,” and “plane” are considered as postulates but they are also undefined in Euclidean geometry. These form the basis of developing other deeper concepts of geometry about shapes and other aspects.

For example, when we claim that a circle is a “set of points equidistant from a given point”, then we are using a line in conception. The amount of measurement that is drawn from the centre to the circumference of the circle is called the radius. Indeed, if there was no notion of a line, the speaking of this distance or the nature of the circle’s circumference would not be apparent.

The fact that in the definition of a circle “line” is listed as an undefined term is important in other branches of circle geometry as well. When introducing concepts such as tangent lines, secant lines, and chords, the building blocks of these definitions are based on the understanding of the concept of a line. Just imagine that even if we are to talk about certain measurements such as the radius or diameter of a circle, we are indirectly working with a line segment that is present in the context of the circle.

Realizing that “line” is an undeveloped concept in the definition of a circle also shows the importance of lines in geometry and the fact that all more intricate notions of geometry are based on them.