Triangle Centroid

Geometry Level 2

Let \(a, b, c\) be the side lengths of triangle \(ABC\) above, and let \(d, e, f\) be the distances from its centroid \(O\) to the vertices. (The red lines are the medians.)

What is the ratio \(\dfrac{a^2+b^2+c^2}{d^2+e^2+f^2}?\)

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