Difference between revisions of "Cyclic quadrilateral"

m (Applicable Theorems/Formulae)
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The following theorems and formulae apply to cyclic quadrilaterals:
 
The following theorems and formulae apply to cyclic quadrilaterals:
  
* [[Ptolemy's theorem]]
+
* [[Ptolemy's Theorem]]
 
* [[Brahmagupta's formula]]
 
* [[Brahmagupta's formula]]
  
 
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Revision as of 10:31, 10 July 2006

A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. They occur frequently on math contests/ olmypiads 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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