The Simson Line

% Figure for a Classical Theorem Note
% Article: Simson's Theorem
% Site: Elementary Geometry
% Website: https://elementarygeometry.org/
% Drawing tool: tkz-euclide
% Output format: SVG
% Standard plate: 5:4
% Last verified: 2026-09-07
% Accent target: none
%
% Editable source for public/diagrams/simson-line.svg.
% Prepared for the web edition of this note.
% The production site serves the committed SVG and does not compile TeX.
\documentclass[tikz,border=8pt]{standalone}
\usepackage{tkz-euclide}

\definecolor{egNavy}{HTML}{17243D}
\definecolor{egGray}{HTML}{777671}
\definecolor{egRust}{HTML}{92513F}
\newcommand{\egUseStandardPlateAt}[1]{%
  \pgfresetboundingbox
  \path[use as bounding box]
    ([xshift=-102pt,yshift=-80pt]#1)
    rectangle
    ([xshift=102pt,yshift=80pt]#1);%
}
\newcommand{\egUseStandardPlate}{%
  \coordinate (egPlateCenter) at (current bounding box.center);%
  \egUseStandardPlateAt{egPlateCenter}%
}
\tikzset{
  eg figure/.style={line cap=round,line join=round,every node/.append style={font=\normalsize,text=egNavy}},
  eg main/.style={draw=egNavy,line width=0.75pt},
  eg support/.style={draw=egGray,line width=0.52pt},
  eg support dashed/.style={draw=egGray,line width=0.52pt,dash pattern=on 3pt off 3pt},
  eg accent/.style={draw=egRust,line width=0.75pt},
  eg mark/.style={draw=egNavy,line width=0.50pt}
}

\begin{document}
\begin{tikzpicture}[eg figure,scale=1.0]
  % A uniform similarity preserves the canonical triangle configuration.
  \tkzDefPoint(0,0){S}
  \tkzDefPoint(-0.5,4.2){A0}
  \tkzDefPoint(-3,0){B0}
  \tkzDefPoint(3,0){C0}
  \tkzDefPointBy[homothety=center S ratio 0.7](A0)\tkzGetPoint{A}
  \tkzDefPointBy[homothety=center S ratio 0.7](B0)\tkzGetPoint{B}
  \tkzDefPointBy[homothety=center S ratio 0.7](C0)\tkzGetPoint{C}

  % P lies on the upper-right arc AC of the circumcircle.
  \tkzDefTriangleCenter[circum](A,B,C)\tkzGetPoint{O}
  \tkzDefPointBy[rotation=center O angle -55](A)\tkzGetPoint{P}

  % These are exact perpendicular projections onto the three side lines.
  % F lies on the extension of BA beyond A in this configuration.
  \tkzDefPointBy[projection=onto B--C](P)\tkzGetPoint{D}
  \tkzDefPointBy[projection=onto C--A](P)\tkzGetPoint{E}
  \tkzDefPointBy[projection=onto A--B](P)\tkzGetPoint{F}

  \tkzDrawCircle[eg support](O,A)
  \tkzDrawSegment[eg support dashed](A,F)
  \tkzDrawPolygon[eg main](A,B,C)
  \tkzDrawSegments[eg support dashed](P,D P,E P,F)
  \tkzDrawLine[eg main,add=0.1 and 0.1](F,D)

  \tkzMarkRightAngle[eg mark,size=0.18](P,D,B)
  \tkzMarkRightAngle[eg mark,size=0.18](P,E,A)
  \tkzMarkRightAngle[eg mark,size=0.18](P,F,A)

  \tkzDrawPoints[color=egNavy,fill=egNavy,size=1.6](A,B,C,P,D,E,F)
  \tkzLabelPoints[above left](A)
  \tkzLabelPoints[below left](B)
  \tkzLabelPoints[below right](C)
  \tkzLabelPoints[above right](P)
  \tkzLabelPoints[below left](D)
  \tkzLabelPoints[below left,xshift=-2pt](E)
  \tkzLabelPoints[above right,xshift=2pt](F)
  \egUseStandardPlate
\end{tikzpicture}
\end{document}