KöMaL 2026 C1902

On the smaller arc $AB$ of the circumcircle of square $ABCD$ we pick internal point $E$. Let $E'$ be the reflection of $E$ across the center of the square. Let $F$ and $G$ be the feet of the perpendiculars from $E$ to diagonals $AC$ and $BD$, respectively. We get similarly points $H$ and $I$ from point $E'$. a) Prove that quadrilateral $FGHI$ is a diamond. b) Find the maximum of the area of quadrilateral $FGHI$.