Question 8
In a rectangle $ABCD$ we have $|AB| = a$ and $|BC| = b$, where $a \ge b$. Let $E$ be a point in the interior of side $AB$ such that there is exactly one possibility to choose points $F, G, H$ on the sides $BC, CD, DA$, respectively, in such a way that $EFGH$ is a rectangle, too. Find the ratio of the areas of rectangles $EFGH$ and $ABCD$.