Arc of a circle

Definition

A part of the circumference of a circle is called an arc of the circle.

arc of circle

A circle can be divided into two parts by cutting the circle at two points and each part of the circle is known as an arc of the circle.

Classification

On the basis of length of the arcs, the arcs of a circle can be classified into two types.

  1. Minor arc
  2. Major arc

Example

A circle is cut at two points $I$ and $J$ and the circle is divided into two parts by this process.

1
Minor arc
minor arc of a circle

The meaning of minor is small. So, a small part of the circumference of the circle is called minor arc of the circle.

The length of this arc is small when compared to other in this case. So, this arc is known as a minor arc of the circle.

$I$ and $J$ are two endpoints of the minor arc of the circle.

2
Major arc
major arc of a circle

The meaning of major is big. Therefore, a big part of the circumference of the circle is called major arc of the circle.

The length of this arc is big when compared to other arc. Hence, this arc is known as the major arc of the circle.

$I$ and $J$ are two endpoints of the major arc of the circle.

Representation

The minor and major arcs consist of $I$ and $J$ as their endpoints commonly. So, it is caused to create confusion if both arcs are represented by the same endpoints. Due to this reason, minor and major arcs are denoted by their endpoints but another point on the associated arc is displayed between them to avoid confusion.

minor and major arcs of a circle

$K$ and $L$ are points on minor and major arcs respectively. The symbol ($\Huge ⌢$) is used to represent an arc in mathematics.

The minor arc of a circle is called as $arc \, IKJ$ and it is denoted by $\stackrel{\Huge ⌢}{IKJ}$ in mathematics.

The major arc of a circle is called as $arc \, ILJ$ and it is expressed in mathematics as $\stackrel{\Huge ⌢}{ILJ}$.

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