Question

The radius of a circle is $13cm$ in which a chord of $10cm$ is drawn. Find the distance of the chord from the centre of the circle.

Answer 1

Let $AC=10$ cm is the chord of the circle and therefore, $AB=5$ cm.

The radius $OA=13$ cm and let $OB=x$ cm

Since the perpendicular line drawn from the centre of the circle to a chord bisects the chord therefore, using Pythagoras theorem:

$O{A}^2=O{B}^2+A{B}^2\Rightarrow {13}^2=x^2+5^2\Rightarrow 169=x^2+25\Rightarrow x^2=169-25=144\Rightarrow x=\sqrt{144}=12$

Hence, the distance of the chord from the centre of the circle is $12$ cm.