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/
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A '''cyclic quadrilateral''' is a [[quadrilateral]] that can be inscribed in a [[circle]].  They have a number of interesting properties.
olmypiads due to their interesting properties.
 
  
 
<center>[[image:Cyclicquad2.png]]</center>
 
<center>[[image:Cyclicquad2.png]]</center>
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* [[Ptolemy's Theorem]]
 
* [[Ptolemy's Theorem]]
 
* [[Brahmagupta's formula]]
 
* [[Brahmagupta's formula]]
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[[Category:Definition]]
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[[Category:Geometry]]
  
 
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Revision as of 03:22, 31 January 2016

A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. They have a number of interesting properties.

Cyclicquad2.png

Properties

In cyclic quadrilateral $ABCD$:

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

Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

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