Given P is any point in the interior of the rectangle ABCD. Show BP^2 + PD^2 = AP^2 + CP^2. Is the result the same when P in the exterior of the rectangle?
Let the height of the rectangle be h (=AD=BC) and the width be w (=AB=BC)
Let the vertical projection of P on AB be at distance x from A,
then it is at distance (w-x) from B
Let the horizontal projection of P on AD be at distance y from ...
A relationship between vertices of a rectangle and another point is proven.