Answer-
[tex]\boxed{\boxed{\dfrac{\widehat{BC}}{\widehat{DE}}=\dfrac{3}{4}}}[/tex]
Solution-
We know that arc length is the product of radius and central angle in radian.
i.e [tex]\text{Arc length}=\text{Radius}\times \text{Central angle}[/tex]
Here,
[tex]\theta_{BC}=1.18\ rad,\ \theta_{DE}=2.36\ rad\\\\AD=\dfrac{2}{3}AB\Rightarrow AB=\dfrac{3}{2}AD[/tex]
So,
[tex]\dfrac{\widehat{BC}}{\widehat{DE}}=\dfrac{AB\times 1.18}{AD\times 2.36}[/tex]
[tex]=\dfrac{\frac{3}{2}AD\times 1.18}{AD\times 2.36}[/tex]
[tex]=\dfrac{3\times 1}{2\times 2}[/tex]
[tex]=\dfrac{3}{4}[/tex]
