Both circle A and circle B have a central angle measuring 140°. The ratio of the radius of circle A to the radius of circle B is 2 3 . If the length of the intercepted arc for circle A is 3 4 π, what is the length of the intercepted arc for circle B? A)
6
7
π
B)
7
5
π
C)
7
8
π
Eliminate
D)
9
8
π

Question

19-04-2018
Mathematics

contestada

Both circle A and circle B have a central angle measuring 140°. The ratio of the radius of circle A to the radius of circle B is 2 3 . If the length of the intercepted arc for circle A is 3 4 π, what is the length of the intercepted arc for circle B? A)
6
7
π
B)
7
5
π
C)
7
8
π
Eliminate
D)
9
8
π

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calculista calculista · Answer 1 · 2018-04-29T00:46:03+02:00

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=2/3--------> rB/rA=3/2
LA=(3/4)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-----> [(3/4)π*3/2]----> 9/8π

the answer is
the length of the intercepted arc for circle B is 9/8π