British flag theorem
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In Euclidean geometry, the British flag theorem says that if a point P is chosen inside rectangle ABCD then AP2 + PC2 = BP2 + DP2.
A---w--------B | | | z---P--------x | | | | | | D---y--------C Figure 1
In Figure 1,
- (AP)^2 = (Aw)^2 +(Az)^2
- (PC)^2 = (wB)^2 +(zD)^2
- (BP)^2 = (wB)^2 +(Az)^2
- (PD)^2 = (zD)^2 +(Aw)^2
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