Both circle a and circle b have a central angle measuring 135°. the ratio of the radius of circle a to the radius of circle b is 4/7. if the length of the intercepted arc for circle a is 1/2π, what is the length of the intercepted arc for circle b?

Let 
rA> radius of the circle A
rB> radius of the circle B
LA> the length of the intercepted arc for circle A
LB> the length of the intercepted arc for circle B

we have that
rA/rB=4/7> rB/rA=7/4
LA=(1/2)π

we know that
if Both circle A and circle B have a central angle , the ratio of the radius of circle A to the radius of circle B is equals to the ratio of the length of circle A to the length of circle B
rA/rB=LA/LB> LB=LA*rB/rA> [(1/2)π*7/4]> 7/8π

the answer is
the length of the intercepted arc for circle B is 7/8π