VMO 1962 Problem 3

Let $ABCD$ is a tetrahedron. Denote by $A'$ , $B'$ the feet of the perpendiculars from $A$ and $B$ , respectively to the opposite faces. Show that $AA'$ and $BB'$ intersect if and only if $AB$ is perpendicular to $CD$ . Do they intersect if $AC = AD = BC = BD$ ?