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.