Respuesta :
The circumference of the smaller circle is C = 2*pi*x/3.
We have given that radius ob measures x units
What is the formula for the circumference of the circle ?
circumference of the circle is given by,
[tex]C = 2\times \pi \times R[/tex]
where pi = 3.14
R= radius
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 is given by
[tex]C(B) = 2\times \piOB = 2\times pi\times x[/tex]
The circumference of circle A is given by
[tex]C(A) = 2\times\pi\times OA[/tex]
we know that the circumference of circle B is 3 times the circumference of circle A,
[tex]C(B) = 3\times C(A)[/tex]
replacing the equations for the circumferences
[tex]2\times\pi\times x = 3\times (2\times pi\times OA)[/tex]
We have divide both sides by [tex]2\pi[/tex]we get:
[tex]x = 3\times OA[/tex]
Now we want to solve this for OA, then we need to isolate it,
[tex]x/3 = OA[/tex]
We can conclude that the radius of the smaller circle is equal to x/3.
Then the circumference of circle A is
[tex]C(A) = 2\times pi\times x/3[/tex]
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