3.13: Intersection with $x+y=\pm 2$; perpendicular bisector

The line $x+2y=10$ intersects the two lines satisfying $(x+y)^{2}=4$ at the points $A$ and $B$.

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

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 $D$.