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

D; 15/8 pi feet

Explanation:

15 8 π feet 25 24 π x = 5 2 9 2 x = 15 8 π When circles have the same central angle measure, the ratio of the lengths of the intercepted arcs is the same as the ratio of the radii

Also answering to confirm the answer above me. :)

Answer 2

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