MathDB

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

Problem Statement