Question

A chord of length 6 cm is drawn in a circle of radius 5 cm. Calculate its distance from the centre of the circle.

Answer 1

Let $AB$ be the chord and $O$ be the centre of the circle, as shown in the above figure.
Also, let $OC$ be the perpendicular drawn from $O$ to $AB$
We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.
$\therefore AC=CB$

$=\frac{6}{2}=3cm$

Now, $△OCA$ is a right angled triangle.
Hence, applying the Pythagoras theorem, we get:

$O{A}^2=O{C}^2+A{C}^2$
$\Rightarrow O{C}^2=(5{)}^2-(3{)}^2$ $[OA=\text{radius}=5cm\text{and}AC=3cm]$

$\Rightarrow O{C}^2=16$
$\therefore OC=4cm$

Hence, the distance of the chord from the centre of the circle is $4cm$.