Find largest possible value of $x^2+y^2$ given that $x^2+y^2=2x-2y+2$ 
Let $x, y \in \mathbb R$ such that $x^2+y^2=2x-2y+2$.  Find the largest possible value of $x^2+y^2$.

My attempt:
$x^2+y^2=2x-2y+2$
$(x^2-2x)+(y^2+1)=2$
$(x-1)^2+(y+1)^2=4$
I have no idea how to continue here.  Any help?

By Minkowski (the triangle inequality) we obtain:
$$\sqrt{x^2+y^2}\leq\sqrt{(x-1)^2+(y+1)^2}+\sqrt{1^2+(-1)^2}=2+\sqrt2.$$
Id est, $$x^2+y^2\leq(2+\sqrt2)^2=6+4\sqrt2.$$
The equality occurs for $(x,y)=(1+\sqrt2,-1-\sqrt2),$ which says that we got a maximal value.
