@Kitonum How about this? -10<=b<=-1, ​​​​​​​-10<=d<=10, ​​​​​​​-10<=f<=10.

@vv Thank you very much.

@Kitonum Thank you very much.

@Kitonum How about  tetrahedron (1, 2, 3), (-2, 8, 9), (5, 0, 7), (3, 4, 2)?

@Kitonum I see. Thank you very much.

@vv Thank you very much.
 

@vv I got "Error, invalid power". I use Maple 2018.

@Kitonum Please give Another sphere, that is mean, vertices have not the form (0,0,0), (a, 0, 0), (0, b, 0) and (0,0,c). 

@tomleslie Thank you very much. Now, I understand.

@Kitonum 
 

My computer runs longer than.
 

@vv Your method very fast. 

@vv If feel, It seems lost solutions.

@vv I do not think so. Because, the sphere tangent to "edges", not tangent to "line". The edge AB is different the line AB. 

@mmcdara Please post your code.

@Gillee Thank you very much.