Answer
$\dfrac{3}{4}$
Work Step by Step
$l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$
or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$
Here, $r$ represents radius and $d$ is diameter.
Let us consider that $r_A$ and $r_B$ are the radii of circle $A$ and $B$. Since we have the same arc length, we can write:
$\dfrac{60^{\circ}}{360^{\circ}} \times 2 \pi r_A=\dfrac{45^{\circ}}{360^{\circ}} \times 2 \pi r_B$
This gives: $60r_A=45 r_B$
or, $\dfrac{r_A}{r_B}=\dfrac{45}{60}=\dfrac{3}{4}$
