Difference between revisions of "Cyclic quadrilateral"

 
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A Cyclic Quadrilateral is a quadrilateral that can be inscribed in a circle. In a cyclic quadrilateral, opposite angles sum to 180 degrees. They frequently show up on Olympiad tests, and have many special properties such as [[Ptolemy's theorem]].
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'''Cyclic Quadrilaterals''' are quadrilaterals that can be inscribed in circles.  They occur frequently on math contests and olympiads due to their interesting properties.
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=== Properties ===
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In cyclic quadrilateral <math>ABCD</math>:
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* <math>\angle A + \angle C = \angle B + \angle D = {180}^{o}</math>
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* <math>\angle ABD = \angle ACD</math>
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* <math>\angle BCA = \angle BDA</math>
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* <math>\angle BAC = \angle BDA</math>
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* <math>\angle CAD = \angle CBD</math>
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=== Applicable Theorems/Formulae ===
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The following theorems and formulae apply to cyclic quadrilaterals:
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* [[Ptolemy's theorem]]
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* [[Brahmagupta's formula]]

Revision as of 19:18, 18 June 2006

Cyclic Quadrilaterals are quadrilaterals that can be inscribed in circles. They occur frequently on math contests and olympiads due to their interesting properties.

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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