Triangle Centroid

Geometry Level 1

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

What is the ratio a2+b2+c2d2+e2+f2?\dfrac{a^2+b^2+c^2}{d^2+e^2+f^2}?

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