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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)
Let A = (1,2,1)B = (-2,2,-1)C = (1,1,0)if we find length AB = 13length BC = 11length AC = 2thus we see thatAB2 = BC2 + AC2thus ABC is a right angled triangle with hypotenuse AB.In a right angled triangle circumcentre will be at the middle point of hypotenusethus in this question circumcentre = mid point of ABcircumcentre = [(1–2)/2 ,(2+2)/2 , (1–1)/2 ] = ( –1/2 , 2 , 0 )hence proved
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