The ratio of the radius of Circle A to the radius of Circle C
We can translate the last phrase as:

1) \(A_{c} = x*A_{b}\)
2)\(A_{b} = x*A_{a}\)

and doing some math:
\(\frac{A_{c}}{x} = A_{b}\)
replacing the second equation with the last expression:
\(\frac{A_{c}}{x} = x*A_{a}\)
\(\frac{A_{c}}{A_{a}} = x^2\)
using ^(-1) (in order to get the right ratio (A/C)):
\(\frac{A_{a}}{A_{c}} = \frac{1}{x^2}\)
but we know that \(A = \pi * r^{2}\):
\(\frac{\pi * r_{a}^{2}}{\pi * r_{c}^{2}} = \frac{1}{x^2}\)
canceling \(\pi\), and applying the square root:
\(\frac{r_{a}}{r_{c}} = \frac{1}{x}\)

Option C.