# Classifying a Triangle!

Geometry Level 5

In $$\triangle ABC$$, suppose that the points $$M,N$$ lie on the line segment $$BC$$, the point $$P$$ lies on the line segment $$CA$$, and the point $$Q$$ lies on the line segment $$AB$$, such that $$MNPQ$$ is a square. Suppose further that:

$\large{\dfrac{AM}{AN} = \dfrac{AC+\sqrt{2}AB}{AB+\sqrt{2}AC}}$

Then $$\triangle ABC$$ is definitely a:

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