Find the angle subtended at the centre of a circle of radius ‘$a$’ by an arc of length ($\frac{a\pi}{4}$) cm.

Given:

Radius of the circle $=a$.

Length of the arc $=\frac{a\pi}{4}\ cm$

To do:

We have to find the angle subtended at the centre.

Solution:

Let $\theta$ be the angle subtended by the arc at the centre.

This implies,

$2 \pi r \times \frac{\theta}{360^{\circ}}=\frac{a \pi}{4}$

$\Rightarrow 2 \pi a \times \frac{\theta}{360^{\circ}}=\frac{a \pi}{4}$

$\Rightarrow \frac{\theta}{360^{\circ}}=\frac{a \pi}{4} \times \frac{1}{2 \pi a}$

$\Rightarrow \frac{\theta}{360^{\circ}}=\frac{1}{8}$

$\Rightarrow \theta=\frac{360^{\circ}}{8}$

$\Rightarrow \theta=45^{\circ}$

The angle subtended at the centre is $45^{\circ}$.

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Updated on: 10-Oct-2022

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