2023 · Q55
Two equal arcs of different circles C1 and C2 subtend angles of 60° and 75° respectively, at the centres. What is the ratio of the radius of C1 to the radius of C2?
Elementary MathematicsCircles
- A4 : 5
- B5 : 4
- C1 : 1
- D3 : 2
Explanation
Equal arc lengths give r₁θ₁ = r₂θ₂ with angles in radians: θ₁ = 60° = π/3 and θ₂ = 75° = 5π/12. Hence r₁/r₂ = θ₂/θ₁ = (5π/12)/(π/3) = 15/12 = 5/4. The answer is (B) 5:4.