Squared Medians

Geometry Level 4

Triangle \(ABC\) has side lengths \(AB=8\), \(BC=12\) and \(CA=14\). Given that \(D\), \(E\) and \(F\) are midpoints of \(BC\), \(CA\) and \(AB\), respectively. Find the value of \(AD^2+BE^2+CF^2\).

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