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


hide comments
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

tomasznowak: 2015-12-11 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: 2015-12-06 20:49:24

Last edit: 2015-12-13 20:04:50
Kaushik Nath: 2015-01-18 07:38:31

Remember to take care of the decimal places
It should be only 4

Manu Agarwal: 2014-12-12 22:47:34

would anyone suggest me critical test cases . Getting WA even after right answer in sample test cases.

Minsuk Kim: 2014-11-29 05:13:03

weird - I'm getting correct answers for sample test cases but keep on getting wrong answer on submission too .... :(

aky: 2014-10-30 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:2004-05-11
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