(i) To find the midpoint of AB, use the midpoint formula:

\(\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\)

Substitute \(A(2, 5)\) and \(B(5, -1)\):

\(\left( \frac{2 + 5}{2}, \frac{5 + (-1)}{2} \right) = \left( \frac{7}{2}, 2 \right)\)

(ii) First, find the slope of AB:

\(m = \frac{-1 - 5}{5 - 2} = \frac{-6}{3} = -2\)

The slope of the line perpendicular to AB is the negative reciprocal:

\(m_{\perp} = \frac{1}{2}\)

Using point C(8, 6) and the point-slope form:

\(y - 6 = \frac{1}{2}(x - 8)\)

Simplify to get the equation in the form \(ax + by + c = 0\):

\(y - 6 = \frac{1}{2}x - 4\)

\(2y - 12 = x - 8\)

\(x - 2y + 4 = 0\)