Under Consideration
If three spheres meet at a point then use IntersectConic[ <Quadric>, <Quadric> ] two times and Intersect command one time.
I propose that the command is ' Intersect[ <Quadric>, <Quadric>, Quadric> ] '.
I like this idea 
If three spheres meet at a point then use IntersectConic[ <Quadric>, <Quadric> ] two times and Intersect command one time.
I propose that the command is ' Intersect[ <Quadric>, <Quadric>, Quadric> ] '.
With the latest versions of GeoGebra you should be able to remove one step, for quadrics a,b,c you can use
Intersect[Intersect[b,c],a]. In the next release it should work also with switched arguments Intersect[a, Intersect[b,c]]
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