British Flag Theorem

The British flag theorem says that if a point P is chosen inside rectangle ABCD then .

 A---w--------B
 |   |        |
 z---P--------x
 |   |        |
 |   |        |
 D---y--------C      
   Figure 1

The theorem also applies to points outside the square, although the proof is harder to visualize in this case.

Proof

In Figure 1, by the Pythagorean theorem, we have:

• 
• 
• 
• 

Therefore:

• 

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