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

<record version="2" id="1452">
 <title>Gergonne triangle</title>
 <name>GergonneTriangle</name>
 <created>2002-01-08 01:21:37</created>
 <modified>2002-05-17 03:12:57</modified>
 <type>Definition</type>
 <creator id="3" name="drini"/>
 <author id="3" name="drini"/>
 <classification>
	<category scheme="msc" code="51-00"/>
 </classification>
 <synonyms>
	<synonym concept="Gergonne triangle" alias="contact triangle"/>
 </synonyms>
 <related>
	<object name="Triangle"/>
	<object name="GergonnePoint"/>
	<object name="Incircle"/>
	<object name="Incenter"/>
	<object name="Centroid"/>
	<object name="Grafix"/>
 </related>
 <preamble>\usepackage{graphicx}
\usepackage{psfrag} 
\usepackage{bbm}
\newcommand{\Z}{\mathbbmss{Z}}
\newcommand{\C}{\mathbbmss{C}}
\newcommand{\R}{\mathbbmss{R}}
\newcommand{\Q}{\mathbbmss{Q}}
\newcommand{\mathbb}[1]{\mathbbmss{#1}}
\newcommand{\figura}[1]{\begin{center}\includegraphics{#1}\end{center}}
\newcommand{\figuraex}[2]{\begin{center}\includegraphics[#2]{#1}\end{center}}</preamble>
 <content>Let $ABC$ be a triangle and $D,E,F$ where the incircle touches the sides $BC,CA,AB$ respectively. Then triangle $DEF$ is called the \emph{Gergonne triangle} or \emph{contact triangle} of $ABC$.\psfrag{A}{$A$}\psfrag{B}{$B$}\psfrag{C}{$C$}\psfrag{D}{$D$}\psfrag{E}{$E$}\psfrag{F}{$F$}\psfrag{P}{$P$}
\figura{gergonne}</content>
</record>
