Segments $\overline{AB}$, $\overline{AC}$ and $\overline{AD}$ are edges of a cube and $\overline{AG}$ is a diagonal through the center of the cube. Point $P$ satisfies $PB=60\sqrt{10}$, $PC=60\sqrt{5}$, $PD=120\sqrt{2}$ and $PG=36\sqrt{7}$. What is $PA$? (2021 AIME I Problem 6) 
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