Theorem

British Flag Theorem

Geometry

The British Flag Theorem states that for any point in the plane of a rectangle, the sum of the squares of its distances to one pair of opposite corners equals the sum of the squares of its distances to the other pair of opposite corners, regardless of where the point lies. It is a simple consequence of the Pythagorean Theorem applied to the point's perpendicular distances from the rectangle's sides, and its name comes from the crossing diagonal lines used in its standard diagram, reminiscent of the Union Flag.

Facts

Statement

For a point P inside a rectangle ABCD, the sum of the squares of the distances from P to two opposite corners equals the sum for the other two opposite corners. 1

Classification

Statement Form

Identity or Equation 1

Connections

Has Statement Form

Equation

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity

In Branch

Geometry

Source British flag theorem (Wikipedia)

Sources

1. British flag theorem (Wikipedia)

Statement of the theorem
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 to the other two opposite corners.
In Branch: Geometry, Lead sentence
In Euclidean geometry, the British flag theorem says that if a point P is chosen inside a rectangle ABCD then the sum of the squar

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British Flag Theorem

Has Statement Form

In Branch