In the rectangular parallelepiped ABCDA′B′C′D′ we denote by M the center of the face ABB′A′. We denote by M1 and M2 the projections of M on the lines B′C and AD′ respectively. Prove that: a) MM1=MM2 b) if (MM1M2)∩(ABC)=d, then d∥AD; c) ∠(MM1M2),(ABC)=45o⇔BCAB=BB′BC+BCBB′.