Question

Radius of a circle is 34 cm and the distance of the chord from the centre is 30 cm, find the length of the chord.

Answer 1

Let the chord be AB.
O be the centre of the circle.
OC be the perpendicular drawn from the centre to the chord AB.
We know that perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, OC $\perp$ AB.
In $△$OCA,
$$\begin{gathered} {\mathrm{OC}}^2+{\mathrm{AC}}^2={\mathrm{OA}}^2 \\ \Rightarrow {30}^2+{\mathrm{AC}}^2={34}^2 \\ \Rightarrow 900+{\mathrm{AC}}^2=1156 \\ \Rightarrow {\mathrm{AC}}^2=256 \\ \Rightarrow \mathrm{AC}=16\mathrm{cm} \end{gathered}$$
Thus, AB = $2\times \mathrm{AC}=2\times 16=32$.