Question 98
The midpoints of the sides $AB$, $BC$, $CD$, $DA$ of the convex quadrilateral $ABCD$ are $E$, $F$, $G$, respectively $H$.
a) Prove that there exists an unique point $O$ inside the quadrilateral so that the areas of the quadrilaterals $AEOH$, $BFOE$, $CGOF$, $DHOG$ are equal.
b) Locate $O$.
a) Prove that there exists an unique point $O$ inside the quadrilateral so that the areas of the quadrilaterals $AEOH$, $BFOE$, $CGOF$, $DHOG$ are equal.
b) Locate $O$.