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Question: How can I make a triangle with integer coordinates of centroid, oorthocenter and center of the triangle?

Question:How can I make a triangle with integer coordinates of centroid, oorthocenter and center of the triangle?

toandhsp 300
geometry centroid
December 18 2014
1

I have some triangles ABC with vertices

1) A(-13,-5,5), B(-5,11,-11), C(-3,-9,15) has centre of out circle is (3, 3, 3), orthocentre (-27, -9, 3) and centroid (-7, -1, -3). 

2) A(-6,6,-1), B(-5,-1,-3), C(2,10,7) has centre of out circle is (1, 2, 3), orthocentre (-11, 11, -3) and centroid (-3, 5, 1). 

How can I write a program to find a triangle with integer coordinates of vertices, centroid, orthocenter and center of the triangle in geometry 3D? 
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