Cercles inscrit et exinscrits d’un triangle

excenter-circle

Il est possible de modifier et de compiler cet exemple :

\documentclass[border=10pt]{standalone}
\usepackage{tkz-euclide}
\begin{document}
  \begin{tikzpicture}[scale=.5]
  \tkzDefPoints{0/0/A,5/0/B,0.8/4/C}
  \tkzDefSpcTriangle[excentral,name=J](A,B,C){a,b,c} 
  \tkzDefSpcTriangle[intouch,name=I](A,B,C){a,b,c}
  \tkzDefProjExcenter[name=J](A,B,C)(a,b,c){X,Y,Z}

  \tkzDefCircle[in](A,B,C)   \tkzGetPoint{I} \tkzGetSecondPoint{T}  
  \tkzDrawCircles[red](Ja,Xa Jb,Yb Jc,Zc)
  \tkzDrawCircle(I,T) 
  \tkzDrawPolygon[dashed,color=blue](Ja,Jb,Jc)
  \tkzDrawLines[add=2 and 2,line width=1pt](A,C A,B B,C)
  \tkzDrawSegments(Ja,Xa Ja,Ya Ja,Za
                   Jb,Xb Jb,Yb Jb,Zb
                   Jc,Xc Jc,Yc Jc,Zc
                   I,Ia I,Ib I,Ic)
  \tkzMarkRightAngles[size=.2,fill=gray!15](%
        Ja,Za,B
        Ja,Xa,B
        Ja,Ya,C
        Jb,Yb,C
        Jb,Zb,B
        Jb,Xb,C
        Jc,Yc,A
        Jc,Zc,B
        Jc,Xc,C
        I,Ia,B
        I,Ib,C
        I,Ic,A)
  \tkzDrawSegments[blue](Jc,C Ja,A Jb,B)
  \tkzLabelPoints(Xb,Yc,A,B,C,Xa,Xc,Ya,Yb,Ja,Jb,Jc,I)
  \tkzLabelPoints[above right](Za,Zb,Zc)
  \tkzLabelPoints[below](Ia,Ib,Ic)
  \end{tikzpicture}
\end{document}