CIRCLE, a curve consisting of all those points of a plane which lie at a fixed distance from a particular point in the plane, called the centre.
The circle is the simplest and most useful plane curve and alone possesses the property of being exactly alike at all points. If the curve be turned in its plane about its centre, the new posi tion taken up is the same as the original position. This property constitutes the "roundness" of the circle, and distinguishes it from other plane curves. A circle may be traced upon a plane by the continuous movement of a point rigidly connected with the centre, as in the use of compasses, and it is in part the simplicity of this construction which explains the fundamental importance of this curve. The tracing of a circle is a much simpler problem than the tracing of a straight line, since the common method of drawing the latter, with the aid of a ruler, only reproduces the straight line already constructed along the ruler's edge. A differ ence in the use of the word "circle" is observable between the older writers and those of the present century. With the former the word is understood to mean the part of the plane enclosed by the curve, while the curve itself is called the circumference. The latter consider the circle and its circumference identical, ex cept that the latter is often spoken of as the measure of the former; and the enclosed portion of the plane is spoken of as the interior, not as the circle itself.
The straight line joining the centre to a point on the circle, e.g., OP or OQ (fig. 1) is called a radius; from the definition of a circle, the radii drawn to various points on the circle are equal. A straight line drawn through the centre and having its ends on the circle, e.g., EOH (fig. I) is called a diameter; evidently all diam eters of the same circle are equal in length, and twice as long as a radius. A straight line, such as ABC (fig. 1), joining any two points on a circle is called a chord ; and the greatest possible chord is a diameter. The portion of the circle intercepted between two points is called an arc. Any two points on the circle divide it into two arcs; thus, in fig. 1,