A concurrency involving that the feet of an altitude, the centroid and a point on the circumcircle

I usually enjoy overkills but Menelaus' theorem is too much even for my taste, here. enter image description here

Add a couple of points: $M$ as the midpoint of $BC$ and $J$ as the projection of $X$ on $BC$. In the rectangle $AKJX$ the centroid $G$ lies at $\frac{2}{3}$ of the segment joining $A$ with the midpoint of $KJ$, hence it trivially lies on the diagonal $KX$.

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Geometry

Euclidean Geometry

Vectors

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