Difference between revisions of "Cyclic quadrilateral"

m (Cyclic Quadrilateral moved to Cyclic quadrilateral: removed unnecessary capitalization)
(altered first sentence)
Line 1: Line 1:
'''Cyclic Quadrilaterals''' are quadrilaterals that can be inscribed in circles.  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 and olympiads due to their interesting properties.
 +
 
  
 
=== Properties ===
 
=== Properties ===
Line 10: Line 11:
 
* <math>\angle BAC = \angle BDA</math>
 
* <math>\angle BAC = \angle BDA</math>
 
* <math>\angle CAD = \angle CBD</math>
 
* <math>\angle CAD = \angle CBD</math>
 +
  
 
=== Applicable Theorems/Formulae ===
 
=== Applicable Theorems/Formulae ===

Revision as of 18:24, 18 June 2006

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.


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: