Question

In each of the following figures, $O$ is the centre of the circle. Find the values of $x$ and $y$.

Answer 1

Consider the following question.

Using a Pythagoras theorem.

$\left(i\right)AO=30cm$

$AB=16cm$

$AB=BC=y=16cm$

$x=BO=\sqrt{{\left(AO\right)}^2+{\left(AB\right)}^2}$

$=\sqrt{{\left(30\right)}^2+{\left(16\right)}^2}$

$=34cm$

$y=16cm$

$\left(ii\right)AB=12cm$

$BC=5cm$

$CA=\sqrt{{\left(AB\right)}^2+{\left(BC\right)}^2}$

$=\sqrt{{\left(12\right)}^2+{\left(5\right)}^2}$

$=13cm$

$y=\frac{x}{2}$

$=6.5cm$

$\left(iii\right)AB=24cm$

$AO=x$

$OB=18cm$

$AO=x=\sqrt{{\left(AB\right)}^2+{\left(OB\right)}^2}$

$=\sqrt{{\left(24\right)}^2+{\left(18\right)}^2}$

$x=30cm$

$y=24cm$

Hence, this is the required answer.