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
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


Added by:Adam Dzedzej
Date:2004-05-11
Time limit:1s
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