Equal arcs in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centres. The ratio of the radii $r_{1} : r_{2}$ is:

Equal arcs: $l = r_{1}\theta_{1} = r_{2}\theta_{2}$, so $\dfrac{r_{1}}{r_{2}} = \dfrac{\theta_{2}}{\theta_{1}} = \dfrac{110}{65} = \dfrac{22}{13}$. Note the **inverse** relation: smaller angle ↔ larger radius (since the arc length is fixed).