Question 13
G7 (LAT). $O$ is a point inside a convex quadrilateral $ABCD$ of area $S$. $K$, $L$, $M$, and $N$ are interior points of the sides $AB$, $BC$, $CD$, and $DA$ respectively. If $OKBL$ and $OMDN$ are parallelograms, prove that $\sqrt S\ge\sqrt{S_1}+\sqrt{S_2}$, where $S_1$ and $S_2$ are the areas of $ONAK$ and $OLCM$ respectively.