**Problem: **

If a, b, c are the sides of a triangle, then prove that

**Solution:**

“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.

More later,

Nalin Pithwa

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