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

Explanation

Let the radii of the two circles be` r_1​` and `r_2`​.
Let an arc of length I subtend an angle of `60^∘` at the centre of the circle of radius `r_1`​, while let an arc of length I subtend an angle of `75` at the centre of the circle of radius `r_2​`.


Now, `60=(pi)/3`​ radian and `75=(5pi)/12`​ radian

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle (theta)( radian at the centre, then


`theta=l/r​ or l=r(theta)`
​

∴`l=(r_1​pi)/3​ and l=(r_2(5pi))/(12)​`
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