In a circle with centre O, a 6 cm long chord is at a distance of 4 cm from the centre. Find the length of the diameter.

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

According to the question, let's draw a figure.

From the figure,

 ${\mathrm{r}}^2=4^2+3^2$     [By Pythagoras theorem]

$\Rightarrow {\mathrm{r}}^2=25$

$\Rightarrow \mathrm{r}=5$

$\therefore \mathrm{The} \mathrm{diameter} \mathrm{of} \mathrm{the} \mathrm{circle}=2\mathrm{r}=2\times 5=\mathbf{10}\mathbf{ }\mathbf{cm}$