BG-MO 1974 Problem 6

In triangle pyramid $MABC$ at least two of the plane angles next to the edge $M$ are not equal to each other. Prove that if the bisectors of these angles form the same angle with the angle bisector of the third plane angle, the following inequality is true $$8a_1b_1c_1\le a^2a_1+b^2b_1+c^2c_1$$ where $a,b,c$ are sides of triangle $ABC$ and $a_1,b_1,c_1$ are edges crossed respectively with $a,b,c$ .

V. Petkov