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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

User Raycohen
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2 Answers

2 votes

Answer:

The answer is D) 15/8π feet!

Explanation:

User Boedy
by
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1 vote

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

User Leibel
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