Question : The length of the chord AB of a circle is equal to the radius of the circle. What will be the angle subtended by the chord at the centre of the circle?
Option 1: 40°
Option 2: 60°
Option 3: 30°
Option 4: 50°
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Correct Answer: 60°
Solution :
Given that the length of the chord AB (d) is equal to the radius (r), we can substitute r for d in the formula:
$\theta = 2 \times \sin^{-1}(\frac{\text{Length of chord}}{2 \times \text{radius}})$
This simplifies to:
⇒ $\theta = 2 \times \sin^{-1}(\frac{r}{2r})$
⇒ $\theta = 2 \times \sin^{-1}(\frac{1}{2})$
⇒ $\theta = 2 \times 30º$
⇒ $\theta = 60º$
Hence, the correct answer is 60º
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