TETRA  Sphere in a tetrahedron
Of course a Sphere Online Judge System is bound to have some tasks about spheres. So here is one. Given the lengths of the edges of a tetrahedron calculate the radius of a sphere inscribed in that tetrahedron (i.e. a sphere tangent to all the faces).
Input
Number N of test cases in a single line. ( N <= 30 ) Each of the next N lines consists of 6 integer numbers  the lengths of the edges of a tetrahedron separated by single spaces. The edges are not longer than 1000 and for the tetrahedron WXYZ, the order of the edges is: WX, WY, WZ, XY, XZ, YZ.
Output
N lines, each consisting of a real number given with four digits decimal precision equal to the radius of a sphere inscribed in the given tetrahedron.
Example
Input: 2 1 1 1 1 1 1 1000 999 998 5 5 6 Output: 0.2041 1.4189
hide comments
nik12321:
20170413 11:17:10
Why can't we use the formula for volume of a tetrahedron as


scorpion_ajay:
20170113 19:30:35
mathematics!! 

vinit_coder:
20160813 19:21:17
go to http://rigmer.com and search this problem.


pranjalikumar9:
20160520 21:07:29
Calculate area of faces using herons formula and then radius of insphere is a simple formula r=3*v/(a1+a2+a3+a4)


tomasznowak:
20151211 13:58:14
If you have good answers for the example and SPOJ gives "Wrong Answer", then you probably don't include the situation, where one (or more) of the edges is 0. If one is zero, therefore the radius is 0. Your program should also write 0 not as "0", but as "0.0000". 

shubhamg gupta:
20151206 20:49:24
Last edit: 20151213 20:04:50 

Kaushik Nath:
20150118 07:38:31
Remember to take care of the decimal places


Manu Agarwal:
20141212 22:47:34
would anyone suggest me critical test cases . Getting WA even after right answer in sample test cases.


Minsuk Kim:
20141129 05:13:03
weird  I'm getting correct answers for sample test cases but keep on getting wrong answer on submission too .... :( 

aky:
20141030 10:08:07
I am using C math library for sqrt etc and I am getting answer to the second one as 1.4186. Answer to first is correct! What's wrong with this approach? 
Added by:  Adam Dzedzej 
Date:  20040511 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 