Squares on Triangles!!!

$ABC$ 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 $\frac {a^{2}}{b^{2}-c^{2}}$ .