alleryEqual arcs in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centres. The ratio of the radii $r_{1} : r_{2}$ is:
A$22 : 13$
B$13 : 22$
C$65 : 110$
D$110 : 65$
Answer & Solution
Correct answer: A. $22 : 13$
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).
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