Question 122
Suppose $ABCD$ is a cyclic quadrilateral, with side lengths $a = AB$, $b = BC$, $c = CD$, $d = DA$. Prove that its area ($ABCD$) doesn't exceed the following expression
$$
\frac{ab + ac + ad + bc + bd + cd}{6},
$$
with equality iff the quadrilateral is a square.
$$
\frac{ab + ac + ad + bc + bd + cd}{6},
$$
with equality iff the quadrilateral is a square.