# Centroid of triangle ABC

Let $D, E, F$ be midpoints of $BC, CA, AB$. Let $AD, BE, CF$ cuts circumcircle of $ABC$ at $X, Y, Z$.
Prove that $\displaystyle \frac{XD^2}{DA^2}+\frac{YE^2}{EB^2}+\frac{ZF^2}{FC^2}\geq \frac{1}{3}$

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