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If the orthocentre and the centroid of a triangle are at $(5,2,-6)$ and $(9,6,-4)$ respectively, then its circumcentre is
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Verified Answer
The correct answer is:
$(11,8,-3)$
We know that, centroid of triangle is divide the orthocentre to circumcentre is ratio $2: 1$
$$
\begin{array}{cc}
(5,2,-6) \quad(9,6,-4) \quad(x, y, z) \\
\therefore \quad & =\frac{2 x+5}{3} \Rightarrow x=11 \\
6=\frac{2 y+2}{3} \Rightarrow y=8 \\
-4=\frac{2 z-6}{3} \Rightarrow z=-3
\end{array}
$$
$\therefore$ Circumcentre of triangle is $(11,8,-3)$.
$$
\begin{array}{cc}
(5,2,-6) \quad(9,6,-4) \quad(x, y, z) \\
\therefore \quad & =\frac{2 x+5}{3} \Rightarrow x=11 \\
6=\frac{2 y+2}{3} \Rightarrow y=8 \\
-4=\frac{2 z-6}{3} \Rightarrow z=-3
\end{array}
$$
$\therefore$ Circumcentre of triangle is $(11,8,-3)$.
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