If the area of same length in two circles subtend angles of `60^(@)` and `75^(@)` at their centres. Find the ratio of their radii.

Explanation

Let `r_(1)` and `r_(2)` be the radii of the given circles and let their arcs of same length 's' subtend angles of `60^(@)` and `75^(@)` at their centres.
Now, `60^(@)=(60 xx pi/180)^(c ) = (pi/3)^(c )` and `75^(@) = (75 xx pi/180)^( c) = (5pi)/(12)^(c )`
`therefore pi/3=s/s_(1)` and `(5pi)/12=s/r_(2)`
`rArr pi/3 r_(1)=s` and `(5pi)/(12)r_(2) = s rArr pi/3 r_(1) = (5pi)/(12)r_(2) rArr 4r_(1)=5r_(2) rArr r_(1):r_(2)=5:4` Ans.