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Q.

If H, G, S, I are respectively Orthocenter, centroid, circumcentre and Incentre of a triangle formed by the points (1,2,3), (2,3,1) and (3, 1, 2) then H + G + S + I =

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a

(2, 2, 2)

b

(6, 6, 6)

c

(8, 8, 8)

d

(4, 4, 4)

answer is D.

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Detailed Solution

Given that the vertices of a triangle are (1,2,3), (2,3,1) and (3, 1, 2)

Observing the above three points, the triangle formed by the given three points is an equilateral triangle

Centroid of the triangle is G=2,2,2

Since it is an equilateral triangle, all the centers are coincident

hence, H+G+S+I=8,8,8

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