Here it is, ANY help would be appreciated.

If ABCD is a rectangle and P is any point its interior, prove AP˛+PC˛

=PB˛+PD˛

Printable View

- Aug 30th 2009, 10:27 AMMp5xm8Need Some Help With A Super Hard Geometry Question
Here it is, ANY help would be appreciated.

If ABCD is a rectangle and P is any point its interior, prove AP˛+PC˛

=PB˛+PD˛ - Aug 30th 2009, 11:11 AMearboth
1. Draw a sketch.

2. Those line segments which have the same length are labeled by the same letter.

3. According to the Pythagorean theorem you get:

$\displaystyle \overline{AP}^2+\overline{PC}^2 = r^2 + t^2 +s^2 + u^2$

$\displaystyle {\color{white}\overline{AP}^2+\overline{PC}^2} = \underbrace{r^2 + u^2}_{\overline{PD}^2} + \underbrace{t^2 +s^2}_{\overline{PB}^2}$