1

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(1). Two bisectors must be drawn from the two vertices A and B so that they intersect at P. (2). BUT the other bisector drawn from the vertex C must be terminated before intersecting P.

    \documentclass[11pt,a4paper]{article}
    \usepackage{blindtext}
    \usepackage{tikz}
    \usepackage{tkz-euclide}
    \usetkzobj{all}
    \usepackage{color}

 \begin{document}
 \normalsize{\textbf{Theorem 1.24.} \textit{The bisectors of the angles of a triangle meet in a point which is equally distant from the sides.}}
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A}
\tkzDefPoint(12,0){B}
\tkzLabelPoints[below](A)
\tkzLabelPoints[below](B)
\tkzDrawSegment(A,B)
\tkzDefPoint(6,7){C}
\tkzLabelPoints[above](C)
\tkzDrawSegment(A,C)
\tkzDrawSegment(B,C)
\end{tikzpicture}
\end{center}
\end{document}
2
\documentclass[11pt,a4paper]{article}
\usepackage{blindtext}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usepackage{color}

\begin{document}

\normalsize{\textbf{Theorem 1.24.} \textit{The bisectors of the angles of a triangle meet in a point which is equally distant from the sides.}}
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A}
\tkzDefPoint(12,0){B}
\tkzLabelPoints[below](A)
\tkzLabelPoints[below](B)
\tkzDrawSegment(A,B)
\tkzDefPoint(6,7){C}
\tkzLabelPoints[above](C)
\tkzDrawSegment(A,C)
\tkzDrawSegment(B,C)

\tkzDefLine[bisector](C,B,A)
\tkzGetPoint{i}
\tkzDefLine[bisector](B,A,C)
\tkzGetPoint{j}
\tkzInterLL(A,j)(B,i) 
\tkzGetPoint{P}
\tkzLabelPoints[below](P)
\tkzDrawBisector(C,B,A)(P)
\tkzDrawBisector(C,A,B)(Q)
\tkzDrawSegment[add=0pt and -30pt](C,P)
\end{tikzpicture}
\end{center}

\end{document}

enter image description here

Remarks:

  • Change -30pt in

    \tkzDrawSegment[add=0pt and -30pt](C,P)
    

    to get the desired shortening for the segment from C to P.

  • Instead of the manual markup for your theorems, you should consider using a dedicated package such as amsthm or ntheorem: A little example with amsthm:

    \documentclass[11pt,a4paper]{article}
    \usepackage{blindtext}
    \usepackage{tikz}
    \usepackage{tkz-euclide}
    \usetkzobj{all}
    \usepackage{color}
    \usepackage{amsthm}
    
    \newtheorem{theo}{Theorem}
    
    \begin{document}
    
    \begin{theo}
    The bisectors of the angles of a triangle meet in a point which is equally distant from the sides.
    \end{theo}
    \begin{center}
    \begin{tikzpicture}
    \tkzDefPoint(0,0){A}
    \tkzDefPoint(12,0){B}
    \tkzLabelPoints[below](A)
    \tkzLabelPoints[below](B)
    \tkzDrawSegment(A,B)
    \tkzDefPoint(6,7){C}
    \tkzLabelPoints[above](C)
    \tkzDrawSegment(A,C)
    \tkzDrawSegment(B,C)
    
    \tkzDefLine[bisector](C,B,A)
    \tkzGetPoint{i}
    \tkzDefLine[bisector](B,A,C)
    \tkzGetPoint{j}
    \tkzInterLL(A,j)(B,i) 
    \tkzGetPoint{P}
    \tkzLabelPoints[below](P)
    \tkzDrawBisector(C,B,A)(P)
    \tkzDrawBisector(C,A,B)(Q)
    \tkzDrawSegment[add=0pt and -30pt](C,P)
    \end{tikzpicture}
    \end{center}
    
    \end{document}
    
  • I appreciate your suggestions. I was used to manually markup the theorems. Your description and coding are very clear! – Nisal Kevin Kotinkaduwa Feb 16 '15 at 5:11
  • 1
    @NisalKevinKotinkaduwa I see. I added to my answer a little example using amsthm to define a theo environment for theorems. Notice that the code is shorter, the formatting is done automatically and, moreover, now you can cross-reference your theorems. – Gonzalo Medina Feb 16 '15 at 5:15
  • @GonzaloMedine You made it extremely simply. I must start using the package amsthm for I have prove a lot of theorems. This package will help enormously. – Nisal Kevin Kotinkaduwa Feb 16 '15 at 5:19

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