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An orthodiagonal quadrilateral is a quadrilateral with perpendicular diagonals or with a perpendicular pair of opposite sides (red lines).

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A cyclic quadrilateral has vertices that lie on a circle (shown in black).

A rational quadrilateral has rational sides and diagonals.

If , , are rational numbers, then two rational cyclic orthodiagonal quadrilaterals can be constructed, with either

,

,

,

,

,

,

or

,

,

,

,

,

.

These formulas generate all such quadrilaterals. The Demonstration uses the first set of formulas.

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Contributed by: Minh Trinh Xuan (May 8)
Open content licensed under CC BY-NC-SA

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