Difference between revisions of "Cyclic quadrilateral"

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A '''cyclic quadrilateral''' is a [[quadrilateral]] that can be inscribed in a circle.  They occur frequently on math contests and olympiads due to their interesting properties.
 
A '''cyclic quadrilateral''' is a [[quadrilateral]] that can be inscribed in a circle.  They occur frequently on math contests and olympiads due to their interesting properties.
  
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<center>[[image:Cyclicquad2.png]]</center>
  
=== Properties ===
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== Properties ==
  
 
In cyclic quadrilateral <math>ABCD</math>:
 
In cyclic quadrilateral <math>ABCD</math>:
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=== Applicable Theorems/Formulae ===
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== Applicable Theorems/Formulae ==
  
 
The following theorems and formulae apply to cyclic quadrilaterals:
 
The following theorems and formulae apply to cyclic quadrilaterals:
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* [[Ptolemy's theorem]]
 
* [[Ptolemy's theorem]]
 
* [[Brahmagupta's formula]]
 
* [[Brahmagupta's formula]]
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Revision as of 14:29, 24 June 2006

A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. They occur frequently on math contests and olympiads due to their interesting properties.

Cyclicquad2.png

Properties

In cyclic quadrilateral $ABCD$:

  • $\angle A + \angle C = \angle B + \angle D = {180}^{o}$
  • $\angle ABD = \angle ACD$
  • $\angle BCA = \angle BDA$
  • $\angle BAC = \angle BDA$
  • $\angle CAD = \angle CBD$


Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

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