Q.Two arcs of the same lengths subtend angles of $60°$ and $75°$ at the centres of two circles. What is the ratio of radii of two circles?

Step 1: Equal arc lengths: $r_1\theta_1 = r_2\theta_2$ (angles need not be converted to radian since they appear as a ratio, and the π/180 factor cancels). …

Set r₁θ₁ = r₂θ₂ (equal arc lengths) and solve for the ratio r₁ : r₂, which is the …

• Inverting the ratio the wrong way round (writing r₁:r₂ = θ₁:θ₂ instead of θ₂:θ₁).
• Unnecessarily converting the angles to radian first (not wrong, but easy to make an arithmetic slip that a ratio c …