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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 $k$.

 Mar 19, 2020
 #1
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Not readable, change it to LaTeX or something that makes the question easier to understand clearly.

 Mar 19, 2020
 #2
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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

Guest Mar 19, 2020
 #3
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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 \(k\)

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 Mar 24, 2020
edited by Guest  Mar 24, 2020
edited by Guest  Mar 24, 2020

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