If arcs of same length in two circles subtend angles of `60^0a n d75^0` at their centers, find the ratios of their radii.

Explanation

Let radius of first circle be `r_(1)` and radius of second circle be `r_(2)` cm.
Angle subtended by arc of first circle at center `theta_(1)=60^(@)`
then length of arc `l_(1) = r_(1)theta_(1)`
Angle subtended by arc of second circle at center `theta_(2)=75^(@)`
then length of arc `l_(2)=r_(2)theta_(2)`.
`therefore` According to the problems, length of arcs are same.
`therefore l_(1)=l_(2)`
`rArr r_(1)0_(1)= r_(2)theta_(2)`
`rArr r_(1)/r_(2)=r_(2)theta_(2)`
`rArr r_(1)/r_(2) = theta_(2)/theta_(1) = 75^(@)/60^(@)`
`=5/4 =5:4`
Therefore, ratio of radii of circles `r_(1):r_(2)=5:4` Ans.