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

 

विकल्प

• $$5\sqrt{2}$$
• $$10\sqrt{2}$$
• $$\frac{5}{\sqrt{2}}$$
• $$10\sqrt{3}$$

Answer 1

In right ∆OAB,

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

Thus, the length of the chord is

$$10\sqrt{2}$$ cm.

Hence, the correct answer is option B.