SE-SKOLORNAS 1986 Problem 2

The diagonals $AC$ and $BD$ of a quadrilateral $ABCD$ intersect at $O$ . If $S_1$ and $S_2$ are the areas of triangles $AOB$ and $COD$ and S that of $ABCD$ , show that $\sqrt{S_1} + \sqrt{S_2} \le \sqrt{S}$ . Prove that equality holds if and only if $AB$ and $CD$ are parallel.