@Kitonum I have just an equation solve(abs(-2*x+5)+abs(-2*x+9)-x^2+7*x-16 = 0, x); by trying many times. Please write a procedure to solve this problem. 

@Carl Love I found one equation
solve(abs(-2*x+5)+abs(-2*x+9)-x^2+7*x-16 = 0, x);

@vv I am sorry about my edit.

@Carl Love I have just edit my question. I am sorry.

@Kitonum Thank you very much. 

@Kitonum I tried your code and copy all coordinates to LaTeX. I see that, ABCD is not a convex quadrilateral.
 

@Kitonum I find angles to draw in LaTeX. 

@tomleslie Thank you very much.

@tomleslie Now I want to put center of sphere lies at Origin. How can I do that?

@tomleslie Thank you very much.

@Kitonum Thank you very much. The formulas calculate volume can check. 

@Kitonum Can you write a procedure to get message there exits tetrahedron or not? I am surprise when I got the value V (volume). 

@tomleslie Please show radius of each circle in out put.

@tomleslie Thank you very much.

@Kitonum Thank you for your answer. Please help me, If O is incernter of triangle ABC, and three sides 3, 5, 7. How to find coordinaters of A, B, C?