Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
If I understand the question correctly, it is not uniquely determined. – Pandora Mar 25 '11 at 17:32
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
its only defined up to a can use the law of cosines to get the angles – yoyo Mar 25 '11 at 17:34

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.

share|cite|improve this answer
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).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.