Art of Problem Solving
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Cyclic quadrilateral: Difference between revisions

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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/
olmypiads due to their interesting properties.


<center>[[image:Cyclicquad2.png]]</center>
<center>[[image:Cyclicquad2.png]]</center>

Revision as of 23:59, 6 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.

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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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