$ A B $ is a chord of a circle with centre $ O $ and radius $ 4 \mathrm{~cm} . A B $ is of length $ 4 \mathrm{~cm} $. Find the area of the sector of the circle formed by chord $ A B $.

Given:

\( A B \) is a chord of a circle with centre \( O \) and radius \( 4 \mathrm{~cm} . A B \) is of length \( 4 \mathrm{~cm} \).  

To do:

We have to find the area of the sector of the circle formed by chord \( A B \).

Solution:

The radius of the circle with centre $O= 4\ cm$

$\Rightarrow AO=BO=4\ cm$
Length of the chord $AB = 4\ cm$

This implies,

$\mathrm{AOB}$ is an equilateral triangle.

$\angle \mathrm{AOB}=60^{\circ}$

Area of the sector $\mathrm{AOB}=\pi r^{2} \times \frac{\theta}{360^{\circ}}$

$=\pi(4)^{2} \times \frac{60^{\circ}}{360^{\circ}} \mathrm{cm}^{2}$

$=16 \pi \times \frac{1}{6}$

$=\frac{8 \pi}{3} \mathrm{~cm}^{2}$

The area of the sector of the circle formed by chord \( A B \) is $\frac{8 \pi}{3} \mathrm{~cm}^{2}$.

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Updated on: 10-Oct-2022

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