# IMO selected problem

Geometry Level 4

$F(x,y)=\sqrt{(x+1)^2+(y-1)^2}+\sqrt{(x-1)^2+(y+1)^2}+\sqrt{(x+2)^2+(y+2)^2}$ Let the minimum of the expression above is $$S$$. If $$S^{2}=k+m\sqrt{n}$$, where $$n$$ is square free, find $$m+k+n$$.

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