Question

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

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=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