Question

Area of the circle in which a chord of length \(\sqrt{2}\) makes an angle \(\pi/2\) at the centre is

• A. \(\pi/2\) sq units
• B. \(2\pi\) sq units
• C. \(\pi\) sq units
• D. \(\pi/4\) sq units

Hint:

Chord length depends on half the central angle.

Answer 1

The Correct Option is C

Step 1: Chord length: \[ l=2R\sin\frac{\theta}{2} \]
Step 2: Given \(\theta=\pi/2\), \[ \sqrt2=2R\sin\frac{\pi}{4}=2R\cdot\frac1{\sqrt2} \Rightarrow R=1 \]
Step 3: \[ \text{Area}=\pi R^2=\pi \]