To find the radius of the original circle before dilation, you can use the scale factor. The relationship between the original radius \( r \) and the dilated radius \( r' \) is given by:
\[ r' = k \cdot r \]
where \( k \) is the scale factor. In this case, the dilated radius \( r' = 9 \) inches and the scale factor \( k = \frac{3}{4} \).
Rearranging the formula to solve for \( r \), we get:
\[ r = \frac{r'}{k} \]
Substituting the known values:
\[ r = \frac{9 \text{ inches}}{\frac{3}{4}} \]
To divide by a fraction, you multiply by its reciprocal:
\[ r = 9 \text{ inches} \times \frac{4}{3} \]
Calculating this:
\[ r = 9 \times \frac{4}{3} = \frac{36}{3} = 12 \text{ inches} \]
So, the radius of the original circle is 12 inches.
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