AoPSWiki

Art of Problem Solving's olympiad training program WOOT starts on Septebmer 8. Train with the top high school students in the the world! Click here to enroll today!

Personal tools

Log in

Search

Toolbox

Cyclic quadrilateral

From AoPSWiki

A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. They have a number of interesting properties.

image:Cyclicquad2.png

Properties

In cyclic quadrilateral $ABCD$ :

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

Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

This article is a stub. Help us out by expanding it.

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/Cyclic_quadrilateral"

Categories: Definition | Geometry | Stubs

Do you have what it takes to be the next brilliant trader, researcher, or developer at Jane Street Capital? Find out in the Careers in Mathematics Forum.

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us