IMO Shortlist 1986 problem 19
Dodao/la:
arhiva2. travnja 2012. A tetrahedron
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
is given such that
![AD = BC = a; AC = BD = b; AB\cdot CD = c^2](/media/m/9/5/2/952a364f1f3a20af0ae0c850d691915e.png)
. Let
![f(P) = AP + BP + CP + DP](/media/m/1/7/e/17e867d2c36435cab062ed56b9151efb.png)
, where
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
is an arbitrary point in space. Compute the least value of
%V0
A tetrahedron $ABCD$ is given such that $AD = BC = a; AC = BD = b; AB\cdot CD = c^2$. Let $f(P) = AP + BP + CP + DP$, where $P$ is an arbitrary point in space. Compute the least value of $f(P).$
Izvor: Međunarodna matematička olimpijada, shortlist 1986