Question 86
Let $ABCD$ be a rectangle with $|AB| \gt |BC|$. The bisector of the diagonal $AC$ meets the side $CD$ at $E$. The circle with the centre at $E$ and the radius $AE$ meets the segment $AB$ again at $F$. Let $G$ be the orthogonal projection of the point $C$ to the line $EF$. Show that $G$ lies on the diagonal $BD$.