BG-MO 1968 Problem 5

The point $M$ is inside the tetrahedron $ABCD$ and the intersection points of the lines $AM,BM,CM$ and $DM$ with the opposite walls are denoted with $A_1,B_1,C_1,D_1$ respectively. It is given also that the ratios $\frac{MA}{MA_1}$ , $\frac{MB}{MB_1}$ , $\frac{MC}{MC_1}$ , and $\frac{MD}{MD_1}$ are equal to the same number $k$ . Find all possible values of $k$ .

K. Petrov