Difference between revisions of "Cyclic quadrilateral"

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(Properties)
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In cyclic quadrilateral <math>ABCD</math>:
 
In cyclic quadrilateral <math>ABCD</math>:
  
* <math>\angle A + \angle C = \angle B + \angle D = {180}^{o}</math>
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* <math>\angle A + \angle C = \angle B + \angle D = {180}^{o} </math>
 
* <math>\angle ABD = \angle ACD</math>
 
* <math>\angle ABD = \angle ACD</math>
 
* <math>\angle BCA = \angle BDA</math>
 
* <math>\angle BCA = \angle BDA</math>
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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 16:53, 31 May 2021

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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