Coordinated Trouble #3

Geometry Level 4

\(G\quad is\quad the\quad centroid\quad of\quad the\\ triangle\quad having\quad vertices\quad \\ A(3,12),\quad B(6,6),\quad C(9,18).\\ Find\quad the\quad value\quad of\\ { { PA }^{ 2 } }{ +PB }^{ 2 }{ +PC }^{ 2 }{ -GA }^{ 2 }{ -GB }^{ 2 }{ -GC }^{ 2 },\\ where\quad P\quad is\quad (5,10).\)

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