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, \(A\), \(B\), \(C\), \(D\), in order from largest area to smallest area.

The ratio of these four areas can be expressed as \(a:b:c:d\) where \(a\), \(b\), \(c\), \(d\), are all integers and are setwise coprime, but not necessarily pairwise coprime.

Find \(a+b+c+d\)

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