PlanetMath: cyclic quadrilateral

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cyclic quadrilateral

(Definition)

Cyclic quadrilateral.
A quadrilateral is cyclic when its four vertices lie on a circle.

$\includegraphics{quadcyclic}$

A necessary and sufficient condition for a quadrilateral to be cyclic, is that the sum of a pair of opposite angles be equal to $180^\circ$ .

One of the main results about these quadrilaterals is Ptolemy's theorem.

Also, from all the quadrilaterals with given sides , the one that is cyclic has the greatest area. If the four sides of a cyclic quadrilateral are known, the area can be found using Brahmagupta's formula

"cyclic quadrilateral" is owned by drini. [ owner history (1) ]

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Other names:

cyclic

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Cross-references: Brahmagupta's formula, area, sides, Ptolemy's theorem, angles, opposite, sum, necessary and sufficient, circle, lie on, vertices, quadrilateral
There are 41 references to this entry.

This is version 4 of cyclic quadrilateral, born on 2001-10-06, modified 2002-03-09.
Object id is 150, canonical name is CyclicQuadrilateral.
Accessed 22816 times total.

Classification:

AMS MSC:

51-00 (Geometry :: General reference works )

Pending Errata and Addenda

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