KöMaL 2013 B4517

$A \ne B$ are interior points of the quadrant $XY$ centred at $O$. The parallels drawn to the line $OX$ through the points $A$, $B$ intersect the radius $OY$ at the points $A_Y$ and $B_Y$. The lines drawn parallel to line $OY$ intersect the radius $OX$ at $A_X$ and $B_X$. Determine the total area of the quadrilaterals $AA_X B_X B$and $AA_Y B_Y B$ as a function of the length $AB$.