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Trapezoid ABCD has ∠BAD = ∠ADC = 90◦ , AB = x, and DC = y...

Trapezoid ABCD has ∠BAD = ∠ADC = 90◦ , AB = x, and DC = y with x < y. Diagonals AC and BD intersect at X. Point L is on AD and point M is on BC so that LM is parallel to AB and LM passes through X. Determine the length of LM in terms of x and y.

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