Find the ratio of the radii of two circles at the centres of which two equal arcs should angle `30^@` and `70^@`

Explanation

Angle`(theta)` of a circle is given by,

`theta = a/r`, where `a` is arc and `r` is radius.

`:. r = a/theta`

`=>r_1/r_2 = (a_1/theta_1)/(a_2/theta_2)`

It is given, arcs of the circles are equal.

`:. r_1/r_2 = theta_2/theta_1 = 70/30 = 7/3`

So, ratio of radii of two given circles will be `7:3`.