Suppose that circles r and s have a central angle measuring 125°. additionally, circle r has a radius of 2 3 feet and the radius of circle s is 3 4 feet. if the length of the intercepted arc for circle r is 4 9 π feet, what is the length of the intercepted arc for circle s?

Let 
rR> radius of the circle R
rS> radius of the circle S
LR> the length of the intercepted arc for circle R
LS> the length of the intercepted arc for circle S

we have that
rR=2/3 ft
rS=3/4 ft
rR/rS=8/9> rS/rR=9/8
LR=(4/9)π ft

we know that
if Both circle R and circle S have a central angle , the ratio of the radius of circle R to the radius of circle S is equals to the ratio of the length of circle R to the length of circle S

rR/rS=LR/LS> LS=LR*rS/rR> [(4/9)π*9/8]> (1/2)π ft

the answer is
the length of the intercepted arc for circle S is  (1/2)π ft

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