# Difference between revisions of "British Flag Theorem"

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draw((0,85)--(200,85)); | draw((0,85)--(200,85)); | ||

draw((124,0)--(124,150)); | draw((124,0)--(124,150)); | ||

− | label("w",(124,0),(0,-1)); | + | label("$w$",(124,0),(0,-1)); |

− | label("x",(200,85),(1,0)); | + | label("$x$",(200,85),(1,0)); |

− | label("y",(124,150),(0,1)); | + | label("$y$",(124,150),(0,1)); |

− | label("z",(0,85),(-1,0)); | + | label("$z$",(0,85),(-1,0)); |

dot((124,0)); | dot((124,0)); | ||

dot((200,85)); | dot((200,85)); |

## Revision as of 18:55, 30 October 2009

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

The theorem also applies to points outside the rectangle, 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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