The diagram shows triangle \(ABC\) with

\(AC=\sqrt6-\sqrt2,\quad AB=\sqrt6+\sqrt2\)

and angle \(CAB=60^\circ\).

(a) Find the exact length of \(BC\).

(b) Show that

\(\sin ACB=\frac{\sqrt6+\sqrt2}{4}.\)

(c) Show that the perpendicular distance from \(A\) to the line \(BC\) is \(1\).