The line

\(x+2y=10\)

intersects the two lines satisfying the equation

\(|x+y|=2\)

at the points \(A\) and \(B\).

(a) Show that the point \(C(-5,20)\) lies on the perpendicular bisector of the line \(AB\).

(b) The point \(D\) also lies on this perpendicular bisector. \(M\) is the mid-point of \(AB\). The distance \(CD\) is three times the distance \(CM\). Find the possible coordinates of \(D\).