\documentclass{article}

\usepackage{pstricks,pst-plot,color}
\usepackage[margin=0cm,papersize={114px,114px}]{geometry}
\newcommand{\PI}{3.14159\space}
\definecolor{dkgreen}{rgb}{0 .5 0}
\psset{unit=50px}

\renewcommand{\th}{.02\space}
\newcommand{\cth}{.015\space}
\newcommand{\pth}{.01\space}
\newcommand{\ballrad}{0.04}
\newcommand{\perplen}{0.1\space}

\newcommand{\cs}{180 mul \PI div cos\space}
\newcommand{\sn}{180 mul \PI div sin\space}
\newcommand{\cpt}{\space dup \cs exch \sn}

\newcommand{\ptA}{0.5 \PI mul\cpt}
\newcommand{\ptB}{1.3 \PI mul\cpt}
\newcommand{\ptC}{1.8 \PI mul\cpt}
\newcommand{\ptP}{1.0 \PI mul\cpt}
\newcommand{\dashlen}{.03}

\renewcommand{\ln}[4]{\psline[linewidth=\th,linecolor=#3,linestyle=#4,dash=\dashlen]{c-c}(! #1)(! #2)}

% ax ay bx by -> ax-bx ay-by
\newcommand{\subpt}{3 2 roll exch sub 3 1 roll sub exch \space}

% ax ay bx by -> ax+bx ay+by
\newcommand{\addpt}{3 2 roll add 3 1 roll add exch \space}

% ax ay bx by -> ax*bx+ay*by
\newcommand{\dotpt}{3 2 roll mul 3 1 roll mul add \space}

% ax ay c -> c*ax c*ay
\newcommand{\scpt}{dup 3 1 roll mul 3 1 roll mul exch \space}

% ax ay -> ax ay ax ay
\newcommand{\duppt}{dup 3 2 roll dup 4 1 roll exch \space}

\newcommand{\normpt}{\duppt \duppt \dotpt sqrt 1 exch div \scpt}

\newcommand{\perppt}[3]
{
  #2 #1 \subpt \duppt #3 #1 \subpt \dotpt
  #2 #1 \subpt \duppt \dotpt
  div
  \scpt
  #1
  \addpt
}

\newcommand{\ptN}{\perppt{\ptA}{\ptB}{\ptP}}
\newcommand{\ptM}{\perppt{\ptC}{\ptA}{\ptP}}
\newcommand{\ptL}{\perppt{\ptB}{\ptC}{\ptP}}

\newcommand{\pt}[4]
{
  \pscircle[linewidth=0,linestyle=none,fillstyle=solid,fillcolor=#2](! #1){\ballrad}
  \uput{.07}[#3](! #1){#4}
}
\newcommand{\ha}[2]{#1 #2 \subpt \normpt \perplen \scpt #2 \addpt}

\newcommand{\plang}[3]
{
  \psline[linewidth=\pth,linecolor=black]{c-c}(! \ha{#1}{#2})(! \ha{#1}{#2} \ha{#3}{#2} \addpt #2 \subpt)(! \ha{#3}{#2})
}

\begin{document}
\noindent
\begin{pspicture}(-1.23,-1.04)(1.04,1.22)
  \pscircle[linewidth=\cth,linecolor=black](0,0){! 1 \cth 2 div add}
  \ln{\ptA}{\ptB}{red}{solid}
  \ln{\ptC}{\ptB}{red}{solid}
  \ln{\ptA}{\ptC}{red}{solid}
  \ln{\ptB}{\ptL}{red}{dashed}
  \ln{\ptL}{\ptP}{dkgreen}{solid}
  \ln{\ptL}{\ptP}{dkgreen}{solid}
  \ln{\ptM}{\ptP}{dkgreen}{solid}
  \ln{\ptN}{\ptP}{dkgreen}{solid}
  \ln{\ptL}{\ptM}{blue}{solid}
  \pt{\ptA}{red}{u}{$A$}
  \pt{\ptB}{red}{d}{$B$}
  \pt{\ptC}{red}{r}{$C$}
  \pt{\ptL}{blue}{d}{$L$}
  \pt{\ptM}{blue}{r}{$M$}
  \pt{\ptN}{blue}{r}{$N$}
  \pt{\ptP}{dkgreen}{l}{$P$}
  \plang{\ptP}{\ptM}{\ptA}
  \plang{\ptP}{\ptN}{\ptB}
  \plang{\ptP}{\ptL}{\ptC}
\end{pspicture}

\end{document}