If the arcs of the same lengths in two circle | vedclass

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(B) Let $r_{1}$ and $r_{2}$ be the radii of the two circles and $l$ be the length of the arc in both cases.We know that the arc length formula is $l =

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$22: 13$

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(B) Let $r_{1}$ and $r_{2}$ be the radii of the two circles and $l$ be the length of the arc in both cases.We know that the arc length formula is $l = r 	heta$,where $	heta$ is in radians.Given $	heta_{1} = 65^{\circ}$ and $	heta_{2} = 110^{\circ}$.Since the arc lengths are equal,$l = r_{1} 	heta_{1} = r_{2} 	heta_{2}$.Therefore,$\frac{r_{1}}{r_{2}} = \frac{	heta_{2}}{	heta_{1}}$.Substituting the values,$\frac{r_{1}}{r_{2}} = \frac{110^{\circ}}{65^{\circ}} = \frac{110}{65} = \frac{22}{13}$.Thus,the ratio of their radii is $22: 13$.

If the arcs of the same lengths in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centre,find the ratio of their radii.

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