What Is an Arc of a Circle?

Arc of a circle: A circle is formed by combining all points in the plane that are a fixed distance. This distance is called the radius of a circle, and it is located at a fixed point from the centre of a circle. Radius is the line segment that joins a point on the circle to the centre of the circle. Any two radii of a circle have the same length.

An arc is a portion of a curve. An arc usually refers to a part of a circle. A chord, a central angle or an inscribed angle may bisect a circle into two arcs. The minor of the two arcs is called the minor arc.

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Before we try to understand the different parts of a circle, let us know what a circle is. A circle is the locus of a point that moves in a plane such that its distance from a particular fixed point in the plane is always constant.

Arc

An arc of a circle is a continuous piece of a circle. Lets us consider a circle C(O,r). Let A1, A2, A3, A4, A5, and A6 be the points on the circle. In this case, the pieces A1A2, A3A4, A5A6, and A1A3 etc., will be the arcs of the circle C(O,r).

Now, let there be two points on a circle C(O,r) – A and B. It is clear that the circle is divided into two sections. Each of these sections is an arc of the circle. The arc can be denoted from A to B in the counterclockwise direction by AB. The arc in the clockwise direction from B to A is denoted by BA. Students should notice that both the points A and B lie on both BA and AB.

Central Angle

Major and minor arcs of a circle can be defined with the concept of central angles, which are given below:

Minor Arc of a Circle

The collection of points in a circle that lies on the central angle of a circle and the inside of a central angle is called the minor arc of a circle. A minor arc of a circle, can also be defined as a part of the circle which is intercepted by a central angle including the two intersecting points.

Major Arc of a Circle

From the above discussion, it is clear that the length of an arc is closely associated with the central angle of the circle which determines the arc of a circle. The larger the central angle of the circle, the larger the minor arc. Thus, we define the degree measure of an arc in the name of the central angle as given below.

Degree Measure of an Arc

The degree measure of a minor arc is the measure of the central angle that contains the arc. The major arc is 360°. We will subtract the degree measure of the corresponding minor arc from the major arc.
The degree measure of an arc PQ is denoted by m(PQ).
Hence, if the degree measure of an arc PQ is θ°, we will write m(PQ)=θ°
It is clear that, m(PQ)+m(QP)=360° or, ?(??)+?(??)=?[?(?,?)]

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