A troublesome point!

Geometry Level 5

Triangle \(ABC\) has side lengths \(AB=3\), \(BC=4\) and \(AC=5\). Let \(M\) be a point in the triangle. Compute the minimum possible value of \(AM^2+BM^2+CM^2.\) If the answer is of the form \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, submit your answer as \(a+b\).

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