If the circumference of a circle is divided into two parts of different lengths, the shorter part is known as the minor arc while the longer part is known as the major arc.

In the diagram, note that the angle subtended at the centre of the circle by the major arc is  \((2\pi-\theta)\) radians.

• Arc Length \(=r\theta\).
• Where \(r\) is the radius of the circle and \(\theta\) is the angle is radians.

• Arc Length \(=\dfrac{\theta}{360^\circ}\times 2\pi r\).
• Where \(r\) is the radius of the circle and \(\theta\) is the angle in degrees.

 The perimeter of the shaded segment \(APB\) of a circle is given:

\(\text{Perimeter of Segment }APB=\text{Length of Chord }AB+\text{Arc Length }APB\),

or can be write as in the formula below:

where \(r\) is the radius of the sector and \(\theta\) is the angle of the sector.

The diagram shows arc \(AB\) of a circle with centre \(O\).

Find the length of the arc \(AB\).

 Based on the question, the length of the arc \(AB\)

\(\begin{aligned} &=13\text{ cm} \times 2.7 \text{ rad}\\ &=35.1 \text{ cm}. \end{aligned}\)

Given length of \(OA=7\) cm,

Find the perimeter of the shaded segment \(APB\).

[ Use \(\pi=3.142\) ]

Find value of \(\theta\),

\(\begin{aligned} s&=r\theta \\\\ 9&=(7)\theta \\\\ \theta&=\dfrac{9}{7}\text{ rad} .\end{aligned}\)

Convert \(\theta\) to degrees,

\(\begin{aligned} \theta&=\dfrac{9}{7}\text{ rad}\times\dfrac{180^\circ}{3.142} \\\\ &=73.66^\circ .\end{aligned}\)

Find the length of chord \(AB\),

\(\begin{aligned} AB&=2r \sin \dfrac{\theta}{2} \\\\ &=2(7) \sin \begin{pmatrix} \dfrac{73.66}{2} \end{pmatrix} \\\\ &=14 \times \sin 36.83^\circ \\\\ &=14 \times 0. \, 5994 \\\\ &= 8. \,3916 \text{ cm}. \end{aligned}\)

The perimeter of the shaded segment \(APB\),

\(\\ \ = \text{Length of Chord } AB + \text{Arc Length } APB \\\\\)

\(\begin{aligned} &=8. \,3916+9 \\\\ &=17.39 \text{ cm} .\end{aligned}\)

If the circumference of a circle is divided into two parts of different lengths, the shorter part is known as the minor arc while the longer part is known as the major arc.

In the diagram, note that the angle subtended at the centre of the circle by the major arc is  \((2\pi-\theta)\) radians.

• Arc Length \(=r\theta\).
• Where \(r\) is the radius of the circle and \(\theta\) is the angle is radians.

• Arc Length \(=\dfrac{\theta}{360^\circ}\times 2\pi r\).
• Where \(r\) is the radius of the circle and \(\theta\) is the angle in degrees.

 The perimeter of the shaded segment \(APB\) of a circle is given:

\(\text{Perimeter of Segment }APB=\text{Length of Chord }AB+\text{Arc Length }APB\),

or can be write as in the formula below:

where \(r\) is the radius of the sector and \(\theta\) is the angle of the sector.

The diagram shows arc \(AB\) of a circle with centre \(O\).

Find the length of the arc \(AB\).

 Based on the question, the length of the arc \(AB\)

\(\begin{aligned} &=13\text{ cm} \times 2.7 \text{ rad}\\ &=35.1 \text{ cm}. \end{aligned}\)

Given length of \(OA=7\) cm,

Find the perimeter of the shaded segment \(APB\).

[ Use \(\pi=3.142\) ]

Find value of \(\theta\),

\(\begin{aligned} s&=r\theta \\\\ 9&=(7)\theta \\\\ \theta&=\dfrac{9}{7}\text{ rad} .\end{aligned}\)

Convert \(\theta\) to degrees,

\(\begin{aligned} \theta&=\dfrac{9}{7}\text{ rad}\times\dfrac{180^\circ}{3.142} \\\\ &=73.66^\circ .\end{aligned}\)

Find the length of chord \(AB\),

\(\begin{aligned} AB&=2r \sin \dfrac{\theta}{2} \\\\ &=2(7) \sin \begin{pmatrix} \dfrac{73.66}{2} \end{pmatrix} \\\\ &=14 \times \sin 36.83^\circ \\\\ &=14 \times 0. \, 5994 \\\\ &= 8. \,3916 \text{ cm}. \end{aligned}\)

The perimeter of the shaded segment \(APB\),

\(\\ \ = \text{Length of Chord } AB + \text{Arc Length } APB \\\\\)

\(\begin{aligned} &=8. \,3916+9 \\\\ &=17.39 \text{ cm} .\end{aligned}\)