Both circle A and circle B have a central angle measuring 135°. The ratio of the radius of circle A to the radius of circle B is 4/7. If the length of the intercepted arc for circle A is 1/2π, what is the length of the intercepted arc for circle B?
Accepted Solution
A:
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=4/7--------> rB/rA=7/4 LA=(1/2)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-----> [(1/2)π*7/4]----> 7/8π
the answer is the length of the intercepted arc for circle B is 7/8π