(a) Calculate the distance from \(T(-6, 6)\) to the center \(C(8, 4)\):

\((x - 8)^2 + (y - 4)^2 = (-6 - 8)^2 + (6 - 4)^2 = 200\)

\(\sqrt{200} = 10\), hence \(\sqrt{200} > 10\), so \(T\) is outside the circle.

(b) Use the formula for the angle between a tangent and a radius:

\(\text{angle} = \sin^{-1}\left(\frac{10}{10\sqrt{2}}\right) = 45^\circ\)

(c) Find the gradient \(m\) of \(CT\):

\(m = \frac{1}{7}\)

Equation of \(AB\) is \(y - 5 = 7(x - 1)\)

\(y = 7x - 2\)

(d) Substitute \(y = 7x - 2\) into the circle's equation:

\((x - 8)^2 + (7x - 2 - 4)^2 = 100\)

\(50x^2 - 100x = 0\)

\(x = 0\) and \(x = 2\)