**Problem.**

Let ABC be a triangle and be the altitude through A. Prove that

.

(As usual, a, b, c denote the sides BC, CA, AB respectively.)

**Proof.**

The given inequality is equivalent to .

where is the area of triangle ABC. Using the identity

, we see that the inequality to be proved is

(here we use ), which is true. Observe that equality holds iff . QED.

More later,

Nalin Pithwa