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Cyclic quadrilateral

Revision as of 11:26, 17 July 2006 by JBL (talk | contribs) (→‎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.

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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