Answer:
[tex]L=2l[/tex] where [tex]l,L[/tex] denote arc lengths of two circles
Step-by-step explanation:
Let [tex]l,L[/tex] denote arc lengths of two circles, [tex]r,R[/tex] denote corresponding radii and
[tex]\alpha _1\,,\alpha _2[/tex] denote the corresponding central angles.
So,
[tex]l=r\alpha _1[/tex] and [tex]L=R\alpha _2[/tex]
This implies [tex]\alpha _1=\frac{l}{r}[/tex] and [tex]\alpha _2=\frac{L}{R}[/tex]
As each circle has an arc where the measures of the corresponding central angles are the same, [tex]\alpha _1=\alpha _2[/tex]
[tex]\frac{l}{r}=\frac{L}{R}[/tex]
As radius of one circle is twice the radius of the other circle,
[tex]R=2r[/tex]
[tex]\frac{l}{r}=\frac{L}{2r}\\\frac{l}{1} =\frac{L}{2}\\L=2l[/tex]
