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 $r_{2}$.Let an arc of length $l$ subtend an angle of $60^{\circ}$ at the centre of the circle of r

Vedclass · Accepted Answer

$5: 4$

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(B) Let the radii of the two circles be $r_{1}$ and $r_{2}$.Let an arc of length $l$ subtend an angle of $60^{\circ}$ at the centre of the circle of radius $r_{1}$,and an arc of the same length $l$ subtend an angle of $75^{\circ}$ at the centre of the circle of radius $r_{2}$.We know that $l = r 	heta$,where $	heta$ is in radians.Convert the angles to radians:$60^{\circ} = 60 	imes \frac{\pi}{180} = \frac{\pi}{3} 	ext{ radians}$.$75^{\circ} = 75 	imes \frac{\pi}{180} = \frac{5\pi}{12} 	ext{ radians}$.Since the arc lengths are equal,$l = r_{1} 	imes \frac{\pi}{3} = r_{2} 	imes \frac{5\pi}{12}$.Dividing both sides by $\pi$,we get $\frac{r_{1}}{3} = \frac{5r_{2}}{12}$.Therefore,$\frac{r_{1}}{r_{2}} = \frac{5 	imes 3}{12} = \frac{15}{12} = \frac{5}{4}$.The ratio of their radii is $5: 4$.

If in two circles,arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre,find the ratio of their radii.

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