PedalTriangle 2002-11-09 05:25:16 2007-08-12 11:05:55 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) \usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them \usepackage{bbm} % define commands here The \emph{pedal triangle} of any triangle $\triangle ABC$, is the triangle whose vertices are the feet of perpendiculars from $A$, $B$ and $C$ to their opposite sides in $\triangle ABC$. In this figure, the $\triangle DEF$ is the pedal triangle of $\triangle ABC$. \begin{center} \includegraphics{triangle.1.eps} \end{center} In general, for any point $P$ inside a triangle, the \emph{pedal triangle} of $P$ is a triangle whose vertices are the feet of perpendiculars from $P$ to the sides of the triangle. In the following figure, the $\triangle D'E'F'$ is the pedal triangle of $P$ in $\triangle ABC$. \begin{center} \includegraphics{triangle.2.eps} \end{center}