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