A diagonal is constructed in a square.
On the other pair of corners, a line is drawn from one of the two such that it intersects the midpoint of one of the opposite sides.
These two lines divide the square into four regions, , , , , in order from largest area to smallest area.
The ratio of these four areas can be expressed as where , , , , are all integers and are setwise coprime, but not necessarily pairwise coprime.
Find