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P is a point inside the rectangle ABCD. Prove that PA^2 + PC^2 = PB^2 + PD^2

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P is a point inside the rectangle ABCD. Prove that PA2 + PC2 = PB2 + PD2

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Take AB as x axis and AD as y axis, a and b are the sides of the rectangle. 

The coordinates of the points are marked on the picture.

PA2 + PC2 + x2 + y2 + (x – a)2 + (y – b)2

PB2 + PD2 = (x – a)2 + y2 + x2 + (y – b)2

PA2 + PC2 = PB2 + PD2

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