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
