Let the radii of the two circles be r1 and r2 . Let an arc of length l subtend an angle of 60° at the centre of the circle of radiusr1, while let an arc of length l subtend an angle of 75° at the centre of the circle of radius r2
\(Now, \,60° = \frac{\pi}{3} \text{radian and\,75°} =\frac{\pi}{12}\,radian\)
We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then
\(θ=\frac{l}{r}\,or\,l=rθ\)
\(l=\frac{r_1{\pi}}{3}\,and\,l=\frac{r_25{\pi}}{12}\)
\(=\frac{r_1{\pi}}{3}\,and\,l=\frac{r_25{\pi}}{12}\)
\(r_1=\frac{r_25}{4}\)
\(\frac{r_1}{r_2}=\frac{5}{4}\)
Thus, the ratio of the radii is 5:4.