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Show that (-1/2,2,0) is the circum centre of the triangle formed by the points(1,2,1),(-2,2,-1),(1,1,0)

Show that (-1/2,2,0) is the circum centre of the triangle formed by the points(1,2,1),(-2,2,-1),(1,1,0)

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Grade:12

1 Answers

Arun
25750 Points
6 years ago
Let A = (1,2,1)B = (-2,2,-1)C = (1,1,0)
if we find length AB = \sqrt13
length BC = \sqrt11
length AC = \sqrt2
thus we see that
AB2 = BC2 + AC2
thus ABC is a right angled triangle with hypotenuse AB.
In a right angled triangle circumcentre will be at the middle point of hypotenuse
thus in this question circumcentre  = mid point of AB
circumcentre = [(1–2)/2 ,(2+2)/2 , (1–1)/2 ]
 = ( –1/2 , 2 , 0 )
hence proved

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