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Correção de rotulagem e alinhamento

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Correção de rotulagem e alinhamento

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(1). A figura deve estar centralizada. (2). Os pontos Ze Xdevem Yser devidamente rotulados. (Observe que os pontos estão distantes de onde deveriam estar.

 \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(3,7){C}
 \tkzLabelPoints[above](C)
 \tkzDrawSegment(A,C)
 \tkzDrawSegment(B,C)
 \tkzDefLine[bisector](A,C,B)\tkzGetPoint{Z}
 \tkzDrawSegment[add=0pt and -150pt](C,Z)
 \tkzLabelPoints[xshift=-10pt](Z)
 \tkzDefLine[bisector](C,A,B)\tkzGetPoint{Y}
 \tkzDrawSegment[add=0pt and -280pt](A,Y)
 \tkzLabelPoints[xshift=-10pt](Y)
 \tkzDefLine[bisector](C,B,A)\tkzGetPoint{X}
 \tkzDrawSegment[add=0pt and -280pt](B,X)
\tkzLabelPoints[xshift=-10pt](X)
\end{tikzpicture}
\end{center}
\end{document}

Responder1

Já tinha uma versão inicial, mas segundo comentários, a intenção era outra. De qualquer forma, decidi incluir aqui as duas versões:

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

\begin{document}

\begin{center}
\begin{tikzpicture}[scale=0.75]
\tkzDefPoint(0,0){A}
\tkzDefPoint(12,0){B}
\tkzLabelPoints[below](A)
\tkzLabelPoints[below](B)
\tkzDrawSegment(A,B)
\tkzDefPoint(3,7){C}
\tkzLabelPoints[above](C)
\tkzDrawSegment(A,C)
\tkzDrawSegment(B,C)

\tkzDrawBisector[dashed,draw=gray](C,B,A)
\tkzGetPoint{X}
\tkzLabelPoints[left](X)

\tkzDrawBisector(A,C,B)
\tkzGetPoint{Z}
\tkzLabelPoints[below](Z)

\tkzDrawBisector(C,A,B)
\tkzGetPoint{Y}
\tkzLabelPoints[above right](Y)

\tkzInterLL(A,Y)(C,Z) 
\tkzGetPoint{P}
\tkzLabelPoints[left](P)

\tkzDrawSegment[add=0pt and -20pt](B,P)
\end{tikzpicture}
\end{center}

\begin{center}
\begin{tikzpicture}[scale=0.75]
\clip
  (-1,-3) rectangle (13,8);
\tkzDefPoint(0,0){A}
\tkzDefPoint(12,0){B}
\tkzLabelPoints[below](A)
\tkzLabelPoints[below](B)
\tkzDrawSegment(A,B)
\tkzDefPoint(3,7){C}
\tkzLabelPoints[above](C)
\tkzDrawSegment(A,C)
\tkzDrawSegment(B,C)

\tkzDefLine[bisector](A,C,B)
\tkzGetPoint{Z}
\tkzDrawSegment[add=0pt and -150pt](C,Z)

\tkzDefLine[bisector](B,A,C)
\tkzGetPoint{Y}
\tkzDrawSegment[add=0pt and -320pt](A,Y)

\tkzDefLine[bisector](C,B,A)
\tkzGetPoint{X}
\tkzDrawSegment[add=0pt and -300pt](B,X)

\tkzInterLL(A,Y)(C,Z) 
\tkzGetPoint{P}
\tkzLabelPoints[left](P)

\tkzLabelLine[pos=0.65](C,Z){Z}
\tkzLabelLine[pos=0.40](B,X){X}
\tkzLabelLine[pos=0.50](A,Y){Y}
\end{tikzpicture}
\end{center}

\end{document}

O resultado:

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