If the vertices of the triangles are ( 1 , 2 , 3 ) , ( 2 , 3 , 1 ) , ( 3 , 1 , 2 ) and if H , G , S and I respectively denote its orthocenter, centroid, circumcenter and incenter, then H + G + S + I =

Question

If the vertices of the triangles are ( 1 , 2 , 3 ) , ( 2 , 3 , 1 ) , ( 3 , 1 , 2 ) and if H , G , S and I respectively denote its orthocenter, centroid, circumcenter and incenter, then H + G + S + I =, ( 2 , 2 , 2 ), ( 4 , 4 , 4 ), ( 6 , 6 , 6 ), ( 8 , 8 , 8 )

MARKS App · Accepted Answer

Distance between x , y , z & a , b , c is x - a 2 + y - b 2 + z - c 2 . A B = 1 + 1 + 4 = 6 B C = 1 + 1 + 4 = 6 A C = 4 + 1 + 1 = 6 So it is an equilateral triangle H = S = I = G = 1 + 2 + 3 3 , 2 + 3 + 1 3 , 3 + 1 + 2 3 ≡ 2 , 2 , 2 ⇒ H + S + I + G = 2 + 2 + 2 , 2 + 2 + 2 , 2 + 2 + 2 = 8 , 8 , 8

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