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