Problem

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Tags: geometry



$2.$Let $ABC$ be an acute-angeled triangle , non-isosceles and with barycentre $G$ (which is , in fact , the intersection of the medians).Let $M$ be the midpoint of $BC$ , and let Ω be the circle with centre $G$ and radius $GM$ , and let $N$ be the point of intersection between Ω and $BC$ that is distinct from $M$.Let $S$ be the symmetric point of $A$ with respect to $N$ , that is , the point on the line $AN$ such that $AN=NS$. Prove that $GS$ is perpendicular to $BC$