Answer:
The circumference of the smaller circle is:
C = 2*pi*x/3
Step-by-step explanation:
We know that for a circle of radius R the circumference is given by:
C = 2*pi*R
where pi = 3.14...
Here we have two circles, A and B, where B is the larger circle and A is the smaller circle.
We know that:
The circumference of B is 3 times the circumference of A.
The radius of circle B is: OB = x
The radius of circle A is: OA
We want to find an expression of OA.
The circumference of circle B will be:
C(B) = 2*pi*OB = 2*pi*x
The circumference of circle A will be:
C(A) = 2*pi*OA
And we know that the circumference of circle B is 3 times the circumference of circle A, then:
C(B) = 3*C(A)
replacing the equations for the circumferences, we get:
2*pi*x = 3*(2*pi*OA)
dividing both sides by 2*pi, we get:
x = 3*OA
Now we want to solve this for OA, then we need to isolate it,
x/3 = OA
We can conclude that the radius of the smaller circle is equal to x/3.
Then the circumference of circle A is:
C(A) = 2*pi*x/3
