KZ-MO 2006 Problem 6

In the tetrahedron $ABCD$ from the vertex $A$ , the perpendiculars $AB '$ , $AC'$ are drawn, $AD '$ on planes dividing dihedral angles at edges $CD$ , $BD$ , $BC$ in half. Prove that the plane $(B'C'D ')$ is parallel to the plane $(BCD)$ .