Let A, B, C and D be four non coplanar points, G the center of gravity of the triangle BCD and M a point on AG. Let P, Q and R be the intersections of the lines AB, AC and AD with the planes (CDM), (BDM) and (BCM).

a) Prove that AM\GM=3×AR\DR

b) Prove that (PQR) || (BCD).