Do keep in mind that there is a basic command-driven interface behind 
Geogebra as well. You can actually literally enter the following into their 
"3D Calculator":

A=(1,2,3)
B=(4,5,6)
L=Segment(A, B)
P=Midpoint(L)
r=Length(L)
C=Circle(P, r)

where the system automatically translates the last command (which does not 
fully determine a circle in 3-space) to:

C: Circle(P,r,xOyPlane)

It looks like it's difficult to get at their programmatic interface. They 
do have scripting, which may provide an interface that's a little easier to 
work with.

It may still be that there's a market for this in sagemath/python; or it 
may be an enjoyable recreational project to work on. But before you set off 
on it, it's probably good to know what prior art is available, and it looks 
like at least the start of what you'd be doing is reimplementing a lot of 
the things geogebra already has.

On the python front, it looks like Sympy (which we already include) may 
have a start for you: https://docs.sympy.org/latest/modules/geometry/

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