Cyclic Orthocenter Configuration for Problem 5098

% Editable source for public/diagrams/crux-5098-cyclic-orthocenter.svg.
% This sanitized drawing contains no source problem text or contact information.
% The web build does not compile TeX; export and review the SVG separately.
% Last verified: 2026-08-30
% The selected coordinates depict a case in which the two equivalent
% conditions both hold.
% Accent target: none
% Publication Profile: scale 1.0.
\documentclass[tikz,border=8pt]{standalone}
\usepackage{tkz-euclide}
\usetikzlibrary{calc,angles,quotes}

\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]
  % The seed uses only the circle center, one radius point, and an integer
  % rotation. Reflections then enforce both CB=CD and the displayed
  % equivalent conditions without precomputed high-precision coordinates.
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(2.4,0){C}
  \tkzDefPointBy[rotation=center O angle -106](C)\tkzGetPoint{A}
  \coordinate (T) at (barycentric cs:A=1,C=3);
  \tkzDefPointBy[symmetry=center O](C)\tkzGetPoint{Cminus}
  \tkzDefPointBy[reflection=over O--T](Cminus)\tkzGetPoint{B}
  \tkzDefPointBy[reflection=over O--C](B)\tkzGetPoint{D}

  \tkzDefCircle[circum](B,C,D)
  \tkzGetPoint{Ocircle}
  \tkzDefPointBy[projection=onto B--C](A)
  \tkzGetPoint{A1}
  \tkzDefPointBy[projection=onto A--C](B)
  \tkzGetPoint{B1}
  \tkzDefTriangleCenter[ortho](A,B,C)
  \tkzGetPoint{H}

  \tkzDrawCircle[eg support](Ocircle,B)
  \tkzDrawSegments[eg main](B,C C,A A,D D,B A,A1 D,B1)
  \tkzDrawSegments[eg support](A,B C,D)

  \tkzDrawSegment[eg support dashed](B,B1)

  \tkzMarkSegments[color=egNavy,line width=0.50pt,mark=|,size=3pt](C,B C,D)
  \tkzMarkSegments[color=egNavy,line width=0.50pt,mark=||,size=3pt](A,H H,A1)
  \tkzMarkRightAngle[eg mark,size=0.18](A,A1,C)
  \tkzMarkRightAngle[eg mark,size=0.18](B,B1,A)
  \tkzMarkRightAngle[eg mark,size=0.18](B,D,B1)

  \tkzDrawPoints[color=egNavy,fill=egNavy,size=1.6](A,B,C,D,A1,B1,H)
  \tkzLabelPoint[below](A){$A$}
  \tkzLabelPoint[above left](B){$B$}
  \tkzLabelPoint[right](C){$C$}
  \tkzLabelPoint[below left](D){$D$}
  \tkzLabelPoint[above right](A1){$A_1$}
  \tkzLabelPoint[below right](B1){$B_1$}
  \tkzLabelPoint[left](H){$H$}
  \egUseStandardPlate
\end{tikzpicture}
\end{document}