# Meta-Medians

Geometry Level 5

In a triangle $$ABC$$ the points $$D,E, F$$ are located on sides $$AB,BC,$$ and$$CA$$ respectives so that $$\frac{AF}{AB}= \frac{BD}{BC}=\frac{CE}{CA}=\frac{1}{3}$$. Find the value of the ratio $\frac{AD^2+BE^2+CF^2}{AB^2+BC^2+CA^2}$

If the result is in the form $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, report $$a+b$$.

Inspiration: Triangle Centroid by Worranat Pakornrat

Note: Drawing is not to scale.

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