Given a tetrahedron ABCD and inside the tetrahedron points K,L,M,N that do not lie on a plane. Denote also the centroids of P, Q, R, S of the tetrahedrons KBCD, ALCD, ABMD, ABCN do not lie on a plane. Let T be the centroid of the tetrahedron ABCD, To be the centroid of the tetrahedron PQRS and T1 be the centroid of the tetrahedron KLMN.a) Prove that the points T,T0,T1 lie in one straight line.
b) Determine the ratio ∣T0T∣:∣T0T1∣. geometrytetrahedron3D geometrycollinear