# Difference between revisions of "Cyclic quadrilateral"

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− | + | '''Cyclic Quadrilaterals''' are quadrilaterals that can be inscribed in circles. They occur frequently on math contests and olympiads due to their interesting properties. | |

+ | |||

+ | === Properties === | ||

+ | |||

+ | In cyclic quadrilateral <math>ABCD</math>: | ||

+ | |||

+ | * <math>\angle A + \angle C = \angle B + \angle D = {180}^{o}</math> | ||

+ | * <math>\angle ABD = \angle ACD</math> | ||

+ | * <math>\angle BCA = \angle BDA</math> | ||

+ | * <math>\angle BAC = \angle BDA</math> | ||

+ | * <math>\angle CAD = \angle CBD</math> | ||

+ | |||

+ | === Applicable Theorems/Formulae === | ||

+ | |||

+ | The following theorems and formulae apply to cyclic quadrilaterals: | ||

+ | |||

+ | * [[Ptolemy's theorem]] | ||

+ | * [[Brahmagupta's formula]] |

## Revision as of 19:18, 18 June 2006

**Cyclic Quadrilaterals** are quadrilaterals that can be inscribed in circles. They occur frequently on math contests and olympiads due to their interesting properties.

### Properties

In cyclic quadrilateral :

### Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals: