Difference between revisions of "British Flag Theorem"
(New page: The '''British flag theorem''' says that if a point P is chosen inside rectangle ABCD then <math>AP^{2}+PC^{2}=BP^{2}+DP^{2}</math>. A---w--------B | | | z---P--------x...) |
|||
| Line 26: | Line 26: | ||
[[Category:geometry]] | [[Category:geometry]] | ||
| + | |||
| + | [[Category:Theorems]] | ||
{{stub}} | {{stub}} | ||
Revision as of 20:34, 14 October 2007
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:
This article is a stub. Help us out by expanding it.
