# Fantastic Ratios

Level pending

Let $$ABCD$$ be a square and $$N$$ a point on segment $$CD$$ such that $$AD = 3 ND$$. Let $$M$$ be a point on segment $$BC$$ satisfying $$\angle MAN = 45^\circ$$. The ratio $$\frac{AM}{AN}$$ can be expressed as $$\frac{a\sqrt{b}}{c}$$, where $$a, b,$$ and $$c$$ are positive integers, $$a$$ and $$b$$ are relatively prime, and $$c$$ is squarefree. Find the value of $$ac - b^2$$.

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