<?xml version="1.0" encoding="UTF-8"?>

<record version="3" id="153">
 <title>Brahmagupta's formula</title>
 <name>BrahmaguptasFormula</name>
 <created>2001-10-06 18:20:34</created>
 <modified>2001-10-31 00:12:51</modified>
 <type>Theorem</type>
 <creator id="3" name="drini"/>
 <author id="3" name="drini"/>
 <classification>
	<category scheme="msc" code="51-00"/>
 </classification>
 <related>
	<object name="CyclicQuadrilateral"/>
	<object name="HeronsFormula"/>
 </related>
 <keywords>
	<term>Area</term>
	<term>Quadrilateral</term>
	<term>Cyclic</term>
 </keywords>
 <preamble>\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
</preamble>
 <content>If a cyclic quadrilateral has sides $p,q,r,s$ then its area is given by
$$\sqrt{(T-p)(T-q)(T-r)(T-s)}$$
where $T=\frac{p+q+r+s}{2}$.

Note that if $s\to 0$, Heron's formula is recovered.

\begin{center}
\includegraphics{quadcyclic}
\end{center}</content>
</record>
