If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Asked by Pragya Singh | 1 year ago |  102

##### Solution :-

Let the radii of the two circles be r1 and r2 . Let an arc of length l1 subtends an angle of 60° at the centre of the circle of radius r1 , whereas let an arc of length l2
subtends an angle of 75° at the centre of the circle of radius r2.

Now, we have,

$$60°=\dfrac{\pi}{3}radian$$

$$75°=\dfrac{5\pi}{12}radian$$

We know that,

in a circle of radius r unit, if an angle θ radian at the centre is subtended by an arc of length l unit then

$$θ=\dfrac{1}{r}$$

l=rθ

Hence we obtain,

$$1= \dfrac{r_1\pi}{3}$$ and

$$1= \dfrac{r_25\pi}{12}$$

according to the question

11 =12

thus we have,

$$\dfrac{r_1\pi}{3\pi}=\dfrac{r_25\pi}{12}$$

$$r_1=\dfrac{r_25}{4}$$

$$\dfrac{r_1}{r_2}=\dfrac{5}{4}$$

Hence , the ratio of the radii is 5:4

Answered by Abhisek | 1 year ago

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