Cyclic quadrilateral
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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.
![Cyclicquad2.png](https://wiki-images.artofproblemsolving.com//3/3e/Cyclicquad2.png)
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.
- ef=ac+bd (e and f are the diagonals)
Applicable Theorems/Formulae
The following theorems and formulae apply to cyclic quadrilaterals:
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