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Question

If the orthocentre and centroid of a triangle are $$(-3,5,1)$$ and $$(3,3,-1)$$ respectively, then its circumcentre is


A
(6,2,1)
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B
(1,2,0)
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C
(6,2,2)
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D
(6,2,2)
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Solution

The correct option is C $$(6,2,-2)$$
given $$centroid(G)=(3,3,-1)$$
$$orthocenter(H)=(-3,5,1)$$
let $$dircumcenter(S)=(x,y,z)$$
we know that G divides H,S in the ratio $$m:n=2:1$$
therefore $$(3,3,-1)=((\dfrac{mx2+nx}{m+n}),(\dfrac{my2+ny1}{m+n}),(\dfrac{mz2+nz1}{m+n}))$$
$$(3,3,-1)=((\dfrac{2x-3}{3}),(\dfrac{2y+5}{3}),(\dfrac{2z+1}{3}))$$
$$(x,y,z)=(6,2,-2)$$


Mathematics

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