If in two circles,arcs of the same length sub | vedclass

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(B) Let the radii of the two circles be $r_1$ and $r_2$. Given that the arc length $l$ is the same for both circles. The formula for arc length is $l

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$\frac{13}{5}$

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(B) Let the radii of the two circles be $r_1$ and $r_2$. Given that the arc length $l$ is the same for both circles. The formula for arc length is $l = r 	heta$,where $	heta$ is in radians. For the first circle,$l = r_1 	imes (30^{\circ} 	imes \frac{\pi}{180^{\circ}}) = r_1 	imes \frac{\pi}{6}$. For the second circle,$l = r_2 	imes (78^{\circ} 	imes \frac{\pi}{180^{\circ}}) = r_2 	imes \frac{13\pi}{30}$. Since the arc lengths are equal,$r_1 	imes \frac{\pi}{6} = r_2 	imes \frac{13\pi}{30}$. Dividing both sides by $\pi$,we get $\frac{r_1}{6} = \frac{13r_2}{30}$. Therefore,$\frac{r_1}{r_2} = \frac{13 	imes 6}{30} = \frac{13}{5}$.

If in two circles,arcs of the same length subtend angles $30^{\circ}$ and $78^{\circ}$ at the centre,then the ratio of their radii is

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