VMO 1978 Problem 6

Given a rectangular parallelepiped $ABCDA'B'C'D'$ with the bases $ABCD, A'B'C'D'$ , the edges $AA',BB', CC',DD'$ and $AB = a,AD = b,AA' = c$ . Show that there exists a triangle with the sides equal to the distances from $A,A',D$ to the diagonal $BD'$ of the parallelepiped. Denote those distances by $m_1,m_2,m_3$ . Find the relationship between $a, b, c,m_1,m_2,m_3$ .