# Two pegs on a square

Geometry Level 4

A unit square $$ABCD$$ has two points $$M,N$$ inside it (possible on the perimeter) such that $$\overline{MA} + \overline{MB} + \overline{MC} + \overline{NA} + \overline{ND} + \overline{NC}$$ is a minimum.

If $$\overline{MN} = \frac {\sqrt a }{b}$$, then what is the value of $$a+b$$?

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