Relation between all 10 distance of 5 points

[Gerenuk]

If you specify all 6 distances between 4 points A, B, C, D you fix a tetraeder. If you now give three distances AM, BM, CM to a central point M you determine the position of that point within the tetraeder.
So theoretically one could calculate DM now?!

So my question is:
What is the relation between distances
AB, AC, AD, AM, BC, BD, BM, CD, CM, DM
in euclidean space?

 

[Gerenuk]

I actually found the answer myself.
See
http://mathworld.wolfram.com/Distance.html
http://mathworld.wolfram.com/Cayley-MengerDeterminant.html
and think ;)