In triangle \(ABC\), \(D\) is the midpoint of \(AC\) and \( E \) is the midpoint of \(AB\). \(BD\) and \(CE\) are perpendicular to each other and intersect at the point \(G\). If \(AB = 7\) and \(AC = 9\), what is the value of \(BC^2\)?

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