If the arcs of the same length in two circles subtend angels `65^@` and `110^@` at the centre, find the ration of their radii.

Explanation

Let 11 and `r 2` be the radil of the two circles. Given that



`theta_{1}=65^{circ}=frac{pi}{180} times 65=frac{13 pi}{36} text { radian }`



and `theta_{2}=110^{circ}=frac{pi}{180} times 110=frac{22 pi}{36} {radian}`


Let `l` be the length of each of the arc. Then `l=r 1 theta 1=r 2 theta 2`, which gives `frac{13 pi}{36} times r_{1}=frac{22 pi}{36} times r_{2}`, i.e., `frac{r_{1}}{r_{2}}=frac{22}{13}`


Hence `r 1: r 2=22: 13`.