# Squares, Midpoints, and Cosine

Geometry Level 2

$$ABCD$$ is a square. Let $$M$$ and $$N$$ be the midpoints of $$BC$$ and $$CD$$, respectively. If $$\cos \angle MAN$$ can be expressed as $$\frac{m}{n}$$ where $$m$$ and $$n$$ are relatively prime positive integers, what is $$m + n$$?

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