Difference between revisions of "Cyclic quadrilateral"

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 $ABCD$ :

$\angle A + \angle C = \angle B + \angle D = {180}^{o}$
$\angle ABD = \angle ACD$
$\angle BCA = \angle BDA$
$\angle BAC = \angle BDA$
$\angle CAD = \angle CBD$

Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

@@ Line 1: / Line 1: @@
-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]].
+'''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]]

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Difference between revisions of "Cyclic quadrilateral"

Revision as of 18:18, 18 June 2006

Properties

Applicable Theorems/Formulae