Difference between revisions of "Cyclic quadrilateral"
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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. | |
| + | |||
| + | === Properties === | ||
| + | |||
| + | In cyclic quadrilateral <math>ABCD</math>: | ||
| + | |||
| + | * <math>\angle A + \angle C = \angle B + \angle D = {180}^{o}</math> | ||
| + | * <math>\angle ABD = \angle ACD</math> | ||
| + | * <math>\angle BCA = \angle BDA</math> | ||
| + | * <math>\angle BAC = \angle BDA</math> | ||
| + | * <math>\angle CAD = \angle CBD</math> | ||
| + | |||
| + | === Applicable Theorems/Formulae === | ||
| + | |||
| + | The following theorems and formulae apply to cyclic quadrilaterals: | ||
| + | |||
| + | * [[Ptolemy's theorem]] | ||
| + | * [[Brahmagupta's formula]] | ||
Revision as of 18:18, 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 
:
Applicable Theorems/Formulae
The following theorems and formulae apply to cyclic quadrilaterals:
