Question

A chord of a circle of radius 10 cm subtends a right angle at the centre. The length of the chord (in cm) is

(a) $5\sqrt{2}$ (b) $10\sqrt{2}$ (c) $\frac{5}{\sqrt{2}}$ (d) $10\sqrt{3}$ [CBSE 2014]

Answer 1

In right ∆OAB,

$$\begin{gathered} {\mathrm{AB}}^2={\mathrm{OA}}^2+{\mathrm{OB}}^2\left(\mathrm{Pythagoras}\mathrm{Theorem}\right) \\ \Rightarrow {\mathrm{AB}}^2={\left(10\right)}^2+{\left(10\right)}^2\left(\mathrm{OA}=\mathrm{OB}=10\mathrm{cm}\right) \\ \Rightarrow {\mathrm{AB}}^2=100+100=200 \\ \Rightarrow \mathrm{AB}=\sqrt{200}=10\sqrt{2}\mathrm{cm} \end{gathered}$$

Thus, the length of the chord is $10\sqrt{2}$ cm.

Hence, the correct answer is option B.