spoj#TETRA. Sphere in a tetrahedron
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</p>Output: 0.2041 1.4189