Let $r_1, r_2$ and $\theta_1, \theta_2$ be the radii and angles subtended at the centreof two circles respectively. So, $\theta_1$ = 60° = $\left(\frac{\pi}{180}\times 60\right)$ radians = $\frac{\pi}{3}$ radians [Since 1° = π/180 radians] and $\theta_2$ = 60° = $\left(\frac{\pi}{180}\times 75\right)$ radians = $\frac{5\pi}{12}$ radians Let l be the length of the arc, then, l = $r_1\theta_1$ and l = $r_2\theta_2$ ⇒ $r_1\theta_1$ = $r_2\theta_2$ ⇒ $\frac{r_1}{r_2}$ = $\frac{5\pi}{12} \times \frac{3}{\pi}$ = $\frac{5}{4}$ Hence, the required ratio is 5 : 4.