Both circle a and circle b have a central angle measuring 140°. the ratio of the radius of circle a to the radius of circle b is 2 3 . if the length of the intercepted arc for circle a is 3 4 π, 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=2/3> rB/rA=3/2

LA=(3/4)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> [(3/4)π*3/2]> 9/8π

the answer is

the length of the intercepted arc for circle B is 9/8π

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