# Squares on Triangles!!!

Level pending

$$ABC$$ is any triangle. On sides $$AB$$ and $$AC$$, squares $$ABDE$$ and $$ACFG$$ are constructed (on the outside). Let $$I$$ be the point of intersection of $$BF$$ and $$CD$$. Let $$AI$$ meet the side $$BC$$ in $$H$$. If $$\frac {BH}{HC}$$ has a value of $$3$$, then find the value of $$\frac {a^{2}}{b^{2}-c^{2}}$$.

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