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.
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A '''cyclic quadrilateral''' is a [[quadrilateral]] that can be inscribed in a [[circle]].  They have a number of interesting properties.
  
=== Properties ===
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<center>[[image:Cyclicquad2.png]]</center>
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== Properties ==
  
 
In cyclic quadrilateral <math>ABCD</math>:
 
In cyclic quadrilateral <math>ABCD</math>:
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* <math>\angle ABD = \angle ACD</math>
 
* <math>\angle ABD = \angle ACD</math>
 
* <math>\angle BCA = \angle BDA</math>
 
* <math>\angle BCA = \angle BDA</math>
* <math>\angle BAC = \angle BDA</math>
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* <math>\angle BAC = \angle BDC</math>
 
* <math>\angle CAD = \angle CBD</math>
 
* <math>\angle CAD = \angle CBD</math>
  
=== 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:
  
* [[Ptolemy's theorem]]
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* [[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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{{stub}}

Latest 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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