Suppose that circles a and b have a central angle measuring 75°. additionally, circle a has a radius of 5 2 feet and the radius of circle b is 9 2 feet. if the length of the intercepted arc for circle a is 25 24 π feet, what is the length of the intercepted arc for circle b? a) 5 8 π feet b) 8 5 π feet c) 8 15 π feet d) 15 8 π feet

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=5/2 ft
rB=9/2 ft
rA/rB=5/9> rB/rA=9/5
LA=(25/24)π ft
 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> [(25/24)π*9/5]> 15/8π ft
 
the answer is
the length of the intercepted arc for circle B is 15/8π ft