Dibuja tres bisectrices de los tres vértices de un triángulo.

Question

(1). Se deben trazar dos bisectrices desde los dos vértices Ay Bde modo que se intersequen en P. (2). PERO la otra bisectriz trazada desde el vértice Cdebe serterminadoantes de cruzarse 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}

Answer 1

\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}

Observaciones:

• Cambiar -30pten

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

  para obtener el acortamiento deseado para el segmento de Ca P.

• En lugar del marcado manual para sus teoremas, debería considerar usar un paquete dedicado como amsthmo ntheorem: Un pequeño ejemplo con 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}