**(A) Formulae for Length and Area of a Circle**

*r*= radius

*A*= area

*s*= arc length q = angle

*l*= length of chord

**(B) Length of an Arc of a Circle**

**Example 1:**

An arc,

*AB*, of a circle of radius 5 cm subtends an angle of 1.5 radians at the centre. Find the length of the arc

*AB*.

*Solution:**s*=

*r*θ

Length of the arc

*AB*= (5)(1.5) =**7.5 cm**

**Example 2:**

An arc,

*PQ*, of a circle of radius 12 cm subtends an angle of 30° at the centre. Find the length of the arc*PQ*.

*Solution:*Length of the arc

$\begin{array}{l}=12\times {30}^{\circ}\times \frac{\pi}{{180}^{\circ}}\\ =6.283\text{cm}\end{array}$
*PQ***Example 3:**

In the above diagram, find

**(i)**length of the minor arc

*AB*

**(ii)**length of the major arc

*APB*

*Solution:***(i)**length of the minor arc

*AB*=

*r*θ

= (7)(0.354)

=

**2.478 cm****(ii)**Since 360

^{o}= 2π radians, the reflex angle

*AOB*

= (2π – 0.354) radians.

Length of the major arc

*APB*= 7 × (2π – 0.354)

= 7 × [(2)(3.1416) – 0.354]

= 7 × 5.9292

=

**41.5044 cm**

This is truly helpful, thanks.