To find the radius of the original circle before the dilation, you can use the scale factor. A scale factor of \( \frac{1}{5} \) means that the original radius is 5 times larger than the radius of the newly created circle.
Given that the radius of the new circle is 18 cm, you can calculate the original radius \( R \) as follows:
\[ R = \text{New Radius} \times \text{Scale Factor}^{-1} \]
Substituting the values:
\[ R = 18 , \text{cm} \times 5 = 90 , \text{cm} \]
Therefore, the radius of the original circle is 90 cm.