symmedian Symmedian 2002-01-08 00:46:43 2002-05-16 01:05:29 Definition \usepackage{graphicx} %\usepackage{xypic} \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}} On any triangle, the three lines obtained by reflecting the medians in the (internal) angle bisectors are called the \emph{symmedians} of the triangle. \figura{symmed} In the picture, $BX$ is angle bisector and $BM$ a median. The reflection of $BM$ on $BX$ is $BN$, a symmedian. It can be stated as symmedians are isogonal conjugates of medians.