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