If the orthocentre and the centroid of a triangle are $(-3,5,2)$ and $(3,3,4)$ respectively, then its circumcentre is

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Aicharya · Accepted Answer

We know that, in a triangle, if $\mathrm{O}$ is orthocentre, $G$ is centroid and $S$ is circumcentre, then $\mathrm{SG}: \mathrm{G0}=1: 2$ Let circumcentre be $(x, y, z)$. $ \begin{array}{ll} 	herefore & \left(\frac{-3+2 x}{1+2}, \frac{5+2 y}{1+2}, \frac{2+2 z}{1+2}ight)=(3,3,4) \ \Rightarrow & \left(\frac{-3+2 x}{3}, \frac{5+2 y}{3}, \frac{2+2 z}{3}ight)=(3,3,4) \ \Rightarrow & \frac{-3+2 x}{3}=3, \frac{5+2 y}{3}=3, \frac{2+2 z}{3}=4 \ \Rightarrow & \quad x=6, y=2, z=5 \ 	herefore & S(6,2,5) . \end{array} $

If the orthocentre and the centroid of a triangle are $(-3,5,2)$ and $(3,3,4)$ respectively, then its…

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