Question

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?

Answer 1

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