@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?

@Carl Love I replace 3, 5, 7 by 3, 4, 5, I got "Warning, expecting only range variable t in expressions [abs(cx)*cos(t), abs(cx)*sin(t)] to be plotted but found name cx
Warning, data could not be converted to float Matrix".

@Carl Love Thank you very much.

@vv I use Maple 2018. I got

@Kitonum I think, we can remove 

eq := sin(9*x-(1/3)*Pi) = sin(7*x-(1/3)*Pi):

@Carl Love I think
restart;
a := 9*x-(1/3)*Pi:
b := 5*x-(1/6)*Pi:
solve(a = 2*Pi*k+b, x);
solve(a = 2*Pi*k+Pi-b, x);

@Mariusz Iwaniuk 
How to use your code with 
sin(9*x-(1/3)*Pi) = sin(5*x-(1/6)*Pi)?

@nm Yes, k is an Integer. I agree with you.

@tomleslie Thank you vey much.

@tomleslie Thank you very much. A small question. Why I get error when I use nops(evalf(sol)) ?

@Carl Love How can I get the exact of the numbers a, b, c?
By hand, I can prove that, the line Delta passing the point DD and perpendicular to the plane (ABC). And then,

maxS = Distance(A, DD)+Distance(B, DD)+Distance(C, DD);

My code get 

[9.37769297305868754, [a = .801783725149603, b = .534522484467394, c = .267261242390448]]