jmc

From the diagram, it follows that the center of the circle is at the point $(-1,1)$, and one point on the circle is at the point $(1,2)$. By the distance formula, the radius of the circle is $\sqrt{(1-(-1){)}^2+(2-1{)}^2}=\sqrt{2^2+1^2}=\sqrt{5}$. Since the $x^2$ term has coefficient $1$, it follows that $A=1$. The equation of the circle is then given by $(x+1{)}^2+(y-1{)}^2=5$, and expanding, $$x^2+2x+1+y^2-2y+1-5=0⟹x^2+y^2+2x-2y-3=0.$$ Summing, $A+B+C+D=1+2-2-3=\boxed{-2}$.