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.

Answer

`r_1 : r_2 = 22:13`

Explanation

Let `r_1` and `r_2` be the radii of the two circles.

Given that

`theta_1=65^circ=(13pi)/36 "radian"`

`theta_2=110^circ=(22pi)/36 "radian"`

Let `l` be the length of each of the arc.

Then, `l=r_1 theta_1 = r_2 theta_2`.

` (13pi)/36 xx r_1 = (22pi)/36 xx r_2`

`r_1/r_2 = 22/13`

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