# Medians And Areas

Geometry Level 3

Let $$ABC$$ be a triangle with the centroid $$G$$ and medians $$AM, BN, CP$$. Let $$Q$$ be a point on $$AG$$ such that $$AQ=GQ$$. Define $$R,S$$ as the midpoints of $$BG,CG$$ respectively. If $$S(\triangle ABC)=x\cdot S(PQNSMR)$$, what is value of $$x$$?

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