ISL 1995 G7

Let ABCD be a convex quadrilateral and O a point inside it. Let the parallels to the lines BC, AB, DA, CD through the point O meet the sides AB, BC, CD, DA of the quadrilateral ABCD at the points E, F, G, H, respectively. Then, prove that $\sqrt {\left|AHOE\right|} + \sqrt {\left|CFOG\right|}\leq\sqrt {\left|ABCD\right|}$ , where $\left|P_1P_2...P_n\right|$ is an abbreviation for the non-directed area of an arbitrary polygon $P_1P_2...P_n$ .