9709 P13 - Nov 2020 - Q11
634
A circle with centre C has equation \((x - 8)^2 + (y - 4)^2 = 100\).
(a) Show that the point \(T(-6, 6)\) is outside the circle.
Two tangents from \(T\) to the circle are drawn.
(b) Show that the angle between one of the tangents and \(CT\) is exactly \(45^\circ\).
The two tangents touch the circle at \(A\) and \(B\).
(c) Find the equation of the line \(AB\), giving your answer in the form \(y = mx + c\).
(d) Find the \(x\)-coordinates of \(A\) and \(B\).
