Shooting 2 Circles with 1 Trigone

Two lines from point $A$ pass through 2 overlapping circles at their intersection points $D,E$ such that $BE || DG$ and $CD || EF$ , as shown above, and the resulted triangle $AFG$ has the numbers indicating partitioned areas: (yellow) triangle $ABC = 16$ and (green) quadrilateral $DEGF = 45$ .

What is the area of the (blue) quadrilateral $BCED$ ?

Note : Figure not drawn to scale.