Question

C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.

Answer 1

C is the centre of the circle.
Radius = 10 cm
Let the chord be AB.
Distance of the centre to the chord = AB.
CD is perpendiculaar to the chord AB.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
$\mathrm{AD}=\frac{\mathrm{AB}}{2}=\frac{12}{2}=6\mathrm{cm}$
In $△$ACD,
We apply the Pythagoras theorem
$$\begin{gathered} {\mathrm{CD}}^2+{\mathrm{AD}}^2={\mathrm{AC}}^2 \\ \Rightarrow {\mathrm{CD}}^2+6^2={10}^2 \\ \Rightarrow {\mathrm{CD}}^2+36=100 \\ \Rightarrow {\mathrm{CD}}^2=64 \\ \Rightarrow \mathrm{CD}=8\mathrm{cm} \end{gathered}$$
Thus, distance of the chord from the centre is 8 cm.