It can be solved with integer-only arithmetic without divisions: sphere of radius r from D in tetrahedron ABCD touches ABC if sqr(v6(a,b,c,d)) <= sqr(r) * s4(a,b,c), where v6 is 6 times volume of the tetrahedron and s4 is 4 times area squared (all easily calculated with vector arithmetic), but you will get out of long long by this, so use v6(a,b,c,d) <= r * sqrt((double)s4(a,b,c)) instead.

Edited by author 14.11.2010 19:21

Edited by author 14.11.2010 19:22