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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)=((mx2+nxm+n),(my2+ny1m+n),(mz2+nz1m+n))
(3,3,1)=((2x33),(2y+53),(2z+13))
(x,y,z)=(6,2,2)


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