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British Flag Theorem

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Prove: If a point P is chosen inside a rectangle ABCD then the sum of the squares of the Euclidean distances from P to two opposite corners of the rectangle equals the sum of the squares of the Euclidean distances from P to the other two opposite corners of the rectangle. As an equation:
∣AP∣^2+∣CP∣^2=∣BP∣^2+∣DP∣^2

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Recommended age: 16 years old
3 times made

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Turkey

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British Flag TheoremOnline version

Prove: If a point P is chosen inside a rectangle ABCD then the sum of the squares of the Euclidean distances from P to two opposite corners of the rectangle equals the sum of the squares of the Euclidean distances from P to the other two opposite corners of the rectangle. As an equation: ∣AP∣^2+∣CP∣^2=∣BP∣^2+∣DP∣^2

by Özlem Esnaf
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