Question

A chord of length $30cm$ is drawn at a distance of $8cm$ from the centre of a circle. Find out the radius of the circle.

Answer 1

Consider $AB$ as the chord of the circle with $O$ as the centre

Construct $OL\perp AB$

From the figure, we know that $OL$ is the distance from the centre of the chord

It is given that $AB=30cm$ and $OL=8cm$

The perpendicular from the centre of a circle to a chord bisects the chord

So we get

$AL=\frac{1}{2}\times AB$

By substituting the values

$AL=\frac{1}{2}\times 30$

By division $AL=15cm$

Consider $△OLA$

Using the Pythagoras theorem it can be written as

$O{A}^2=O{L}^2+A{L}^2$

By substituting the values we get

$O{A}^2=8^2+{15}^2$

On further calculation

$O{A}^2=64+225$

By addition

$O{A}^2=289$

By taking the square root

$OA=\sqrt{289}$

So we get

$OA=17cm$

Therefore, the radius of the circle is $17cm$