Difference between revisions of "Cyclic quadrilateral"
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* <math>\angle CAD = \angle CBD</math> | * <math>\angle CAD = \angle CBD</math> | ||
* All four [[perpendicular bisector|perpendicular bisectors]] are [[concurrent]]. The converse is also true. This intersection is the [[circumcenter]] of the quadrilateral. | * All four [[perpendicular bisector|perpendicular bisectors]] are [[concurrent]]. The converse is also true. This intersection is the [[circumcenter]] of the quadrilateral. | ||
| + | * Any two opposite sites of the quadrilateral are antiparallel with respect to the other two opposite sites. | ||
== Applicable Theorems/Formulae == | == Applicable Theorems/Formulae == | ||
Revision as of 13:33, 18 October 2023
A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. While all triangles are cyclic, the same is not true of quadrilaterals. They have a number of interesting properties.
Properties
In a quadrilateral 
:
This property is both sufficient and necessary, and is often used to show that a quadrilateral is cyclic.
- All four perpendicular bisectors are concurrent. The converse is also true. This intersection is the circumcenter of the quadrilateral.
- Any two opposite sites of the quadrilateral are antiparallel with respect to the other two opposite sites.
This property is both sufficient and necessary, and is often used to show that a quadrilateral is cyclic.
Applicable Theorems/Formulae
The following theorems and formulae apply to cyclic quadrilaterals:
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