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Math Help - Need Some Help With A Super Hard Geometry Question

  1. #1
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    Need 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˛
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  2. #2
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    Quote Originally Posted by Mp5xm8 View Post
    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˛
    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:

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

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