Two equal arcs of different circles C_{1} and C_{2} subtend angles of 60^{\circ} and 75^{\circ} respectively, at the centres. What is the ratio of the radius of C_{1} to the radius of C_{2}?
- A. 4:5
- B. 5:4 ✓
- C. 1:1
- D. 3:2
Correct Answer: B. 5:4
Explanation
Arc length l = r\theta. Since l_1 = l_2, we have r_1 \theta_1 = r_2 \theta_2. Therefore, r_1 \times 60^{\circ} = r_2 \times 75^{\circ}, giving \frac{r_1}{r_2} = \frac{75}{60} = \frac{5}{4}.
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