IMO 1986 — Shortlisted problems Question 19

(BUL 2) 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 $f(P)$.