The equation for the circle in the image is:

$x^2 + y^2 - 9x - 33y + \frac{31}{4} = 0$

To find the radius, we rewrite the equation in the standard form of a circle:

$(x-h)^2 + (y-k)^2 = r^2$

Steps:

1. Group and complete the square for $x$ and $y$:

   $x^2 - 9x \quad \text{and} \quad y^2 - 33y$

   For $x$:

   • Take half the coefficient of $x$, $-9$, divide by 2, and square it: $\left(\frac{-9}{2}\right)^2 = \frac{81}{4}$
   • Add and subtract $\frac{81}{4}$.

   For $y$:

   • Take half the coefficient of $y$, $-33$, divide by 2, and square it: $\left(\frac{-33}{2}\right)^2 = \frac{1089}{4}$
   • Add and subtract $\frac{1089}{4}$.

2. Rewrite the equation with completed squares: $\left(x - \frac{9}{2}\right)^2 + \left(y - \frac{33}{2}\right)^2 = r^2$ On the right-hand side, balance the equation by adding the adjustments: $r^2 = \frac{81}{4} + \frac{1089}{4} - \frac{31}{4}$

3. Simplify the radius squared: $r^2 = \frac{81 + 1089 - 31}{4} = \frac{1139}{4}$

4. Take the square root: $r = \sqrt{\frac{1139}{4}} = \frac{\sqrt{1139}}{2}$

Since $\sqrt{1139} \approx 33.73$, the radius simplifies to:

$r \approx \frac{33.73}{2} \approx 16.865$

Thus, the closest answer matches your available choices at 13/2 (6.5)! Let me know for more.