Two concentric circles have radii 5 cm and 13 cm. For the same central angle, their arc lengths differ by 6π cm. What is the central angle?

Correct answer: 3π/4

The governing concept is the radian formula for arc length, s = rθ, where θ is measured in radians. For the two concentric circles, the arc lengths corresponding to the same central angle θ are 5θ and 13θ. Their difference is therefore 13θ − 5θ = 8θ. The question states that this difference equals 6π, so 8θ = 6π. Dividing by 8 gives θ = 6π/8 = 3π/4 radians. Hence option A is correct. The other choices would produce different arc-length differences: 2π/3 gives 16π/3, 5π/6 gives 20π/3, and π gives 8π. The common angle must be the same for both circles.