Difference between revisions of "Cyclic quadrilateral"
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| − | A '''cyclic quadrilateral''' is a [[quadrilateral]] that can be inscribed in a circle. They | + | A '''cyclic quadrilateral''' is a [[quadrilateral]] that can be inscribed in a [[circle]]. They have a number of interesting properties. |
| + | <center>[[image:Cyclicquad2.png]]</center> | ||
| − | + | == Properties == | |
In cyclic quadrilateral <math>ABCD</math>: | In cyclic quadrilateral <math>ABCD</math>: | ||
| − | * <math>\angle A + \angle C = \angle B + \angle D = {180}^{o}</math> | + | * <math>\angle A + \angle C = \angle B + \angle D = {180}^{o} </math> |
* <math>\angle ABD = \angle ACD</math> | * <math>\angle ABD = \angle ACD</math> | ||
* <math>\angle BCA = \angle BDA</math> | * <math>\angle BCA = \angle BDA</math> | ||
| − | * <math>\angle BAC = \angle | + | * <math>\angle BAC = \angle BDC</math> |
* <math>\angle CAD = \angle CBD</math> | * <math>\angle CAD = \angle CBD</math> | ||
| − | + | == Applicable Theorems/Formulae == | |
| − | |||
The following theorems and formulae apply to cyclic quadrilaterals: | The following theorems and formulae apply to cyclic quadrilaterals: | ||
| − | * [[Ptolemy's | + | * [[Ptolemy's Theorem]] |
* [[Brahmagupta's formula]] | * [[Brahmagupta's formula]] | ||
| + | |||
| + | [[Category:Definition]] | ||
| + | |||
| + | [[Category:Geometry]] | ||
| + | |||
| + | {{stub}} | ||
Revision as of 16:53, 31 May 2021
A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. They have a number of interesting properties.
Properties
In cyclic quadrilateral 
:
Applicable Theorems/Formulae
The following theorems and formulae apply to cyclic quadrilaterals:
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