The diagonals of a parallelogram A B C...

The diagonals of a parallelogram `A B C D` intersect at `O`. A line through `O` meets `A B\ ` in ` X\ a n d\ C D` in `Y`. Show that `a r\ (q u a d rilateral A X Y D)=1/2a r(paral l e l ogram\ \ A B C D)`

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