Suppose that circles R and S have a central angle measuring 125°. Additionally, circle R has a radius of 2 3 feet and the radius of circle S is 3 4 feet. If the length of the intercepted arc for circle R is 4 9 π feet, what is the length of the intercepted arc for circle S?
Let rR--------> radius of the circle R rS-------> radius of the circle S LR------> the length of the intercepted arc for circle R LS------> the length of the intercepted arc for circle S
we have that rR=2/3 ft rS=3/4 ft rR/rS=8/9--------> rS/rR=9/8 LR=(4/9)π ft
we know that if Both circle R and circle S have a central angle , the ratio of the radius of circle R to the radius of circle S is equals to the ratio of the length of circle R to the length of circle S
rR/rS=LR/LS--------> LS=LR*rS/rR-----> [(4/9)π*9/8]----> (1/2)π ft
the answer is the length of the intercepted arc for circle S is (1/2)π ft
1 2 π feet 4 9 π x = 2 3 3 4 x = 1 2 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.
