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Circle $A$ has a radius that is half the length of circle $B$'s radius. Each circle has an arc with central angle equal to $60$ degrees.

Find the ratio of the arc length that corresponds to that central angle of circle $B$ to circle $A$.

A

$1:2$

B

$2:1$

C

$1:4$

D

$4:1$

E

$6:1$

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