Arc – Geometry

 In mathematics the word arc also used for some other curved shapes like an ellipse but mostly used for a circle.

Definition:                   

An arc is a portion of the circumference of a circle. It is also known as circular arc.

In above figure AB is the arc of the circle.
There are two measures of an arc

1. The length of the arc 2. The angle of the arc

The length of the arc:

Arc length 

An arc is a smooth curve and the length of a arc is known as arc length. 

A chord separates the circumference of a circle into two parts,

1. Major arc 
2. Minor arc 

There are two pieces, one is longer and other is smaller. The longer piece is called the “Major arc” and the smaller piece is called the “Minor arc”.

 The major arc is denoted by          ⌒ 
                                                  PRQ    
                        ⌒
and minor arc is        PQ . 

When the arc length would be measured in distance units, to show the measure of the the arc is preceded by letter L(for length)
                                 ⌒
                                 LAB = 5cm.

Read as the length of the AB is 5 cm.

The formula to measure the arc is

Arc length = 2𝝿r(c/360)

where, C is the central angle of the arc in degree and R is the radius of arc.

Arc length formula- When central angle in radians, the formula will be,

Arc length = R C 

where C is central angle of arc in radians, R is the Radius of the arc. 

The angle of the arc:

The angle formed by the arc at the center of the circle, is measure of the angle.

It shows by letter
  ⌒
 mAB = 30 degree

Read as the arc AB has a measure of 30 degree.

When P and Q are ends of a diameter, then both arcs are equal and each is called a Semicircle.

When the length of an arc is exactly half of the circle, then it is known as a semicircular arc.

It also separates the area of the circle into two segments

1. Major segments
2. Minor segments