Question 77
Let $ABCD$ be a cyclic quadrilateral. The parallel through $A$ to $BD$ meets the parallel through $B$ to $AC$ at the point $E$. The circumcircle of triangle $ABE$ meets the lines $EC$ and $ED$ a second time at the points $F$ and $G$, respectively. Show that the lines $AB$, $CD$ and $FG$ are parallel or concurrent.