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I want a triangle composed of points A, B and C in Cartesian 3D space.

I currently know the positions of points A and B, but I need point C. I have the line segment AB, and thus its magnitude. I have only the magnitudes of line segments AC and BC.

From this data, how do I derive point C? Please explain your logic. Thank you for your help.

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1  
If I understand the question correctly, it is not uniquely determined. –  Pandora Mar 25 '11 at 17:32
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There are an infinite amount of possible point C's. Imagine the intersection of two spheres of radius $|AC|$ coming from point $A$ and radius $|BC|$ coming from point $B$. –  Justin L. Mar 25 '11 at 17:33
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its only defined up to a rotation...you can use the law of cosines to get the angles –  yoyo Mar 25 '11 at 17:34

2 Answers 2

The lengths of segments AB, AC and BC are not enough to uniquely identify a triangle in 3-d space.

You can just pick a random plane that contains AB and make your triangle there.

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Even on a plane, there are two such points for C, and so two triangles. –  Henry Mar 25 '11 at 17:43
    
@Henry: yes, but then it's just a matter of sign-choosing. –  Eelvex Mar 25 '11 at 17:48

The locus of point C is a circle (with a center inside AB) or nothing (depends on magnitudes of segments AC and BC).

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