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.

If arcs of same length in two circles subtend angles of `60^0a n d75^0

1.	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.
Answer» 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.