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|}](/media/m/2/8/e/28e9b2372fbc559dcd37d69b3c2972e2.png)
, where
![\left|P_1P_2...P_n\right|](/media/m/5/2/2/5220a160a91f0246963219bad078c6fa.png)
is an abbreviation for the non-directed area of an arbitrary polygon
![P_1P_2...P_n](/media/m/1/3/8/138c53c71dfb923bfe675dca8cde2742.png)
.
%V0
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 $P_1P_2...P_n$.