To find the radius of the original circle before the dilation, you can use the scale factor of the dilation. The relationship between the original radius (let's denote it as \( r \)) and the dilated radius (which is given as 9 inches) can be expressed as:
\[ \text{dilated radius} = \text{original radius} \times \text{scale factor} \]
Substituting the values we have:
\[ 9 = r \times \frac{3}{4} \]
To isolate \( r \), you can rearrange the equation:
\[ r = 9 \div \frac{3}{4} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ r = 9 \times \frac{4}{3} \]
Now, calculate \( r \):
\[ r = \frac{9 \times 4}{3} = \frac{36}{3} = 12 \]
So, the radius of the original circle is \( \boxed{12} \) inches.