# 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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