*Problem:*

If are side lengths of a triangle, and be its area and circumradius respectively, satisfying the equality , prove that

.

*Solution:*

Let .

Then the given inequality is of the form

.

Removing the square roots of we get that

.

Let us now introduce the , that is

.

Then the inequality takes the form

.

Thus attains its maximum when of the are equal.

So, we need only need to prove the inequality for , or we need to prove that for it holds that

,

which is true, *Q.E.D.*

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