Question 71

An arc of 30° in one circle is double an arc in a second circle, the radius of which is three times the radius of the first. Then the angles subtended by the arc of the second circle at its centre is

Solution

For the first circle, angle subtended = 30° and let radius = $$r$$ cm

For the second circle, let angle subtended = $$\theta$$ and radius = $$3r$$ cm

According to ques, arc of first circle = 2 $$\times$$ arc of second circle

=> $$\frac{30^\circ}{360^\circ} 2 \pi r = 2 \times \frac{\theta}{360^\circ} 2 \pi (3r)$$

=> $$60\pi r = 12 \times \theta \pi r$$

=> $$\theta = \frac{60}{12}=5^\circ$$

=> Ans - (C)

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