Question

Find the length of a chord which is at a distance of $5cm$ from the centre of a circle of radius $13cm$.

Answer 1

Let $BC$ be the chord of the circle and $OA\perp BC.$

By using Pythagoras theorem in $△OAB,$

$\begin{array}{cc}O{A}^2+A{B}^2& =O{B}^2\\ 5^2+A{B}^2& ={13}^2\\ 25+A{B}^2& =169\\ A{B}^2& =169-25\\ & =144\\ AB& =12cm\end{array}$

Perpendicular through the center of the circle bisects the chord of the circle. Hence,

$\begin{array}{cc}BC& =2AB\\ & =2\times 12\\ & =24cm\end{array}$