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)

Dear student
We have,A3,2,-5,B-3,8,-5 and C-3,2,1AB=-3-32+8-22+-5+52=62+62+02=72BC=-3+32+2-82+1+52=62+62=72CA=-3-32+2-22+1+52=62+62=72Since AB=BC=CA,ABC is equilateral triangle.We know that orthocentre,centroid,circumcentre and incentre of equilateral triangle are the same(i.e., all the four points coincide).Now, centroid=3+2-53,-3+8-53,-3+2+13=0,0,0So, circumcentre=0,0,0
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