## TETRA - Sphere in a tetrahedron

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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
```

 < Previous 1 2 3 Next > kaiyu: 2020-06-18 03:14:49 Not a binary search qs! i_0__0_i: 2020-06-15 10:19:54 order of input of edge is sideedge - sideedge - sideedge - baseedge - baseedge - baseedge Last edit: 2020-06-15 10:27:17 black_shroud: 2020-04-26 16:27:06 binary search did the trick :D mohanish2504: 2019-04-14 12:55:31 Do the following: 1.Take six edges a,b,c,d,e,f 2.CALCULATE volume by link given below 3.Calculate 4 surfaces and add them as SurfaceArea 4.Formula for radius of sphere = (3*vol)/SurfaceArea 5.set precision for 4 units and u are done with AC Link for volume: https://awsmcode.files.wordpress.com/2014/04/volume_of_tetrahedron-e1398363175375.png nguyenthihang: 2018-06-09 12:34:33 input 2 1 1 1 1 1 1 1000 999 998 5 5 6 output 0.2041 -nan WHY???? mayankdhyani: 2018-04-07 21:28:54 If sides are equal then apply the formula r(radii of sphere) = [ side*sqrt(6) ] / 12. i got my code wrong but my answer of first condition (1 1 1 1 1 1) was correct. please someone upload full program of this question. I dont understand if sides are different of tetrahedron then how sphere will get into it with same radii ? Last edit: 2018-04-07 21:31:48 nik12321: 2017-04-13 11:17:10 Why can't we use the formula for volume of a tetrahedron as (1/3)*area(base)*height. We can take any face as base and the length of opposite side as height. Tried and gave the wrong answer scorpion_ajay: 2017-01-13 19:30:35 mathematics!! vinit_coder: 2016-08-13 19:21:17 go to http://rigmer.com and search this problem. pranjalikumar9: 2016-05-20 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) where v is volume of tetrahedron.. Solve pyramids before this question