Show that D(-1, 4, -3) is the circumcentre of triangle ABC with vertices A(3, 2, -5), B(-3. 8, -5) and C(-3, 2, 1).
To prove: D is circumcenter of triangle ABC
Let us consider D as circumcenter of triangle ABC.
∴ AD = BC = CD.
Formula:
The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by
D=
Here,
(x1,y1,z1)= (3, 2, -5)
(x2,y2,z2)= (-3. 8, -5)
(x3,y3,z3)= (-3, 2, 1)
(x4,y4,z4) = (-1, 4, -3)
Length AD = 
= 
= 
= 
= 
Length BD = 
= 
= 
= 
= 
Length CD = 
= 
= 
= 
= 
Hence, the condition is consistent.
Hence, D is circumcenter of triangle ABC.
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