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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