Problem

Source: China TST 2004 Quiz

Tags: geometry unsolved, geometry



In convex quadrilateral $ ABCD$, $ AB=a$, $ BC=b$, $ CD=c$, $ DA=d$, $ AC=e$, $ BD=f$. If $ \max \{a,b,c,d,e,f \}=1$, then find the maximum value of $ abcd$.