MATH SOLVE

4 months ago

Q:
# 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

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