If a, b, c are the sides of a triangle, then prove that
“Reverse-engineering” this will not help !! One big hint is to think of cyclic expressions as most identities and inequaltties to triangles have such a nature.
Here you go:
Since a, b, c are the sides of a triangle, then the cyclic sum
But this sum is
By dividing this by 2abc, we get
exactly what we had to prove.
Ref: Problems for the Mathematical Olympiads (From the first team selection test to the IMO) by Andrei Negut.