Coordinated Trouble #2

Geometry Level 3

\( G\quad is\quad the\quad centroid\quad Of\quad the\quad triangle\quad ABC.\\ If\quad X={ GA }^{ 2 }{ +GB }^{ 2 }{ +GC }^{ 2 }\quad \& \quad Y={ { CA }^{ 2 } }{ +AB }^{ 2 }{ +BC }^{ 2 },\\ Find\quad \frac { Y }{ X } . \)

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