To determine the radius of the original circle before dilation, we can use the scale factor.
The formula to find the relationship between the original radius (\( r \)) and the radius after dilation (\( r' \)) is:
\[ r' = \text{scale factor} \times r \]
Given:
- The scale factor is 34.
- The radius of the dilated circle is 9 inches.
We can rearrange the formula to find the original radius (\( r \)):
\[ r = \frac{r'}{\text{scale factor}} \]
Substituting in the values:
\[ r = \frac{9 \text{ inches}}{34} \]
Calculating this gives:
\[ r \approx 0.2647 \text{ inches} \]
So, the radius of the original circle is approximately 0.26 inches.