Proof
Drop perpendicular lines from the point P to the sides of the rectangle, meeting sides AB, BC, CD, and AD in points w, x, y and z respectively, as shown in the figure; these four points wxyz form the vertices of an orthodiagonal quadrilateral. By applying the Pythagorean theorem to the right triangle AwP, and observing that wP = Az, it follows that
and by a similar argument the squared lengths of the distances from P to the other three corners can be calculated as
- and
Therefore:
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