Let $A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$. There exists a point $X$ and a constant $k$ such that for any point $P$, \[PA^2 + PB^2 + PC^2 = 3PX^2 + k.\]Find the constant $k$.
To make it readable: Let \(A=(4,-1)\)\(,B=(6,2),\) and \(C=(-1,2).\)There exists a point \(X\) and a constant \(k\) such that, for any point \(P\)\(PA^2 + PB^2 + PC^2 = 3PX^2 + k\). Find (the value of) constant \(k\)
