Discussion
If in the two circles, arc of same length subtend angle 60° and 75° at the centre, then the ratio of their radii is :
Answer: D
The ratio of the radii is 5 : 4.
Arc length equals radius times the angle in radians, \(l = r\theta\). For the same arc length, the radius is inversely proportional to the angle:
\[ \begin{aligned} r_{1} \times 60 &= r_{2} \times 75 \\ \frac{r_{1}}{r_{2}} &= \frac{75}{60} = \frac{5}{4} \end{aligned} \]
The circle in which the arc makes the smaller angle (60°) has the larger radius. 4 : 5 is the ratio of the angles, the common mistake of treating radius as proportional to angle.
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