(a) Substitute the line equation \(y = 3x - 20\) into the circle equation \((x+1)^2 + (y-2)^2 = 85\).

\((x+1)^2 + (3x-22)^2 = 85\)

Expand and simplify: \(10x^2 - 130x + 400 = 0\)

Factorize: \((x-8)(x-5) = 0\)

Solutions: \(x = 8\) or \(x = 5\)

For \(x = 8\), \(y = 3(8) - 20 = 4\), so \((8, 4)\)

For \(x = 5\), \(y = 3(5) - 20 = -5\), so \((5, -5)\)

(b) Mid-point of \(AB\) is \(\left(\frac{6.5}{2}, -\frac{1}{2}\right)\)

Use \(C = (-1, 2)\)

Calculate \(r^2\): \((-1 - \frac{6.5}{2})^2 + (2 + \frac{1}{2})^2 = 62\frac{1}{2}\)

Equation of the circle: \((x+1)^2 + (y-2)^2 = 62\frac{1}{2}\)