Diagram

The Incenter: Trigonometric Ceva

The completed angle-bisector concurrence figure

The completed angle-bisector concurrence figure for The Incenter through Trigonometric Ceva, with complete source.

Methods Trigonometric Ceva

Drawing tool: tkz-euclideSource available

Completed figures

Triangle ABC with D on BC, E on CA, and F on AB. The three angle-bisector cevians AD, BE, and CF meet at I.
Figure 1. The three internal angle-bisector cevians meet at I.

Complete source

Ceva configuration

% Figure for a Classical Theorem Note
% Article: The Incenter through Trigonometric Ceva
% Site: Elementary Geometry
% Website: https://elementarygeometry.org/
% Drawing tool: tkz-euclide
% Output format: SVG
% Last verified: 2026-08-24
%
% Prepared for the web edition of this note.
% Editable source for public/diagrams/incenter-ceva.svg.
% The web build does not compile TeX; export and review the SVG separately.
\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]
  \tkzDefPoint(-0.5,4.2){A}
  \tkzDefPoint(-3,0){B}
  \tkzDefPoint(3,0){C}
  \tkzDefTriangleCenter[in](A,B,C)\tkzGetPoint{I}
  \tkzInterLL(A,I)(B,C)\tkzGetPoint{D}
  \tkzInterLL(B,I)(C,A)\tkzGetPoint{E}
  \tkzInterLL(C,I)(A,B)\tkzGetPoint{F}

  \tkzDrawSegments[eg support dashed](A,D B,E C,F)
  \tkzDrawSegments[eg main](A,B B,C C,A)
  \tkzDrawPoints[color=egNavy,fill=egNavy,size=1.6](A,B,C,D,E,F,I)
  \tkzLabelPoints[above](A)
  \tkzLabelPoints[below left](B)
  \tkzLabelPoints[below right](C)
  \tkzLabelPoints[below](D)
  \tkzLabelPoints[right](E)
  \tkzLabelPoints[left](F)
  \tkzLabelPoints[below left,xshift=3pt,yshift=-1pt](I)
  \egUseStandardPlate
\end{tikzpicture}
\end{document}

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