Cyclic polygon

From Citizendium, the Citizens' Compendium

Jump to: navigation, search


This article is developing and not approved.
Main Article
Talk
Related Articles  [?]
Bibliography  [?]
External Links  [?]
 
http://en.citizendium.org/wiki?title=Cyclic_polygon&printable=yes
This is a draft article, under development and not meant to be cited but you can help to improve it. These unapproved articles are subject to a disclaimer.

In plane geometry, a cyclic polygon is a polygon whose vertices all lie on one circle. The centre of the circle is the circumcentre of the polygon.

Every triangle is cyclic, since any three (non-collinear) points lie on a unique circle.

Cyclic qusdrilateral

A cyclic quadrilateral is a quadrilateral whose four vertices are concyclic. A quadrilateral is cyclic if and only if pairs of opposite angles are supplementary (add up to 180°, π radians). Ptolemy's theorem states that in a cyclic quadrilateral ABCD, the product of the diagonals is equal to the sum of the two products of the opposite sides:

AC \cdot BD = AB \cdot CD + BC \cdot AD .\,
Retrieved from "http://en.citizendium.org/wiki/Cyclic_polygon"
Views
Personal tools