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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/
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>

Revision as of 09:50, 30 July 2006

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

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Properties

In cyclic quadrilateral $ABCD$:

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

Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

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