Question

In the given figure, $O$ is the centre of the circle with radius $20\text{cm}$ and $OD$ is perpendicular to $AB$. If $AB=32\text{cm}$, find the length of $CD$.

Answer 1

To find: $CD$
Given, $AB=32\text{cm}$
$\Rightarrow AC=16\text{cm}$ (Since $\perp$ drawn from the centre of the chord, bisect the chord)
in right $\Delta OCA$,
$O{A}^2=O{C}^2+A{C}^2$ (By Pythagoras theorem)
$\Rightarrow O{C}^2=O{A}^2-A{C}^2$
$\Rightarrow O{C}^2={20}^2-{16}^2$
$\Rightarrow O{C}^2=144$
$\Rightarrow OC=12\text{cm}$
Since $OD=20\text{cm}$ and $OC=12\text{cm}$
$\Rightarrow CD=OD-OC=20-12=8\text{cm}$