tkz-euclide (9mar20)

git-svn-id: svn://tug.org/texlive/trunk@54200 c570f23f-e606-0410-a88d-b1316a301751

22 files changed, 815 insertions, 397 deletions

diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-euclide.sty b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-euclide.sty
index 5c86e5c0af9..74ab4a29873 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-euclide.sty
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-euclide.sty
@@ -1,30 +1,78 @@
-% tkz-euclide.sty
-% Copyright 2020 by Alain Matthes
+% tkz-euclide.sty (utf8 encoding)
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
 %
-% This file may be distributed and/or modified
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
 %
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
+% This work consists of the files:
+% tkz-euclide.sty
+% tkz-obj-eu-angles.tex
+% tkz-obj-eu-arcs.tex
+% tkz-obj-eu-circles.tex
+% tkz-obj-eu-compass.tex
+% tkz-obj-eu-draw-circles.tex
+% tkz-obj-eu-draw-lines.tex
+% tkz-obj-eu-draw-polygons.tex
+% tkz-obj-eu-lines.tex
+% tkz-obj-eu-points-by.tex
+% tkz-obj-eu-points-rnd.tex
+% tkz-obj-eu-points-with.tex
+% tkz-obj-eu-points.tex
+% tkz-obj-eu-polygons.tex
+% tkz-obj-eu-protractor.tex
+% tkz-obj-eu-sectors.tex
+% tkz-obj-eu-show.tex
+% tkz-obj-eu-triangles.tex
+% tkz-tools-angles.tex
+% tkz-tools-intersections.tex
+% tkz-tools-math.tex
+
 %<------------------------------------------------------------–>
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-euclide.sty} 
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-euclide.sty} 
 \NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{tkz-euclide}[2020/01/24 3.02c  for  euclidan geometry ]
+\ProvidesPackage{tkz-euclide}[2020/03/03 3.05c  for  euclidan geometry ]
 \RequirePackage{tkz-base}
 \makeatletter
-\@ifpackagelater{tkz-base}{2020/01/24}{%
+\@ifpackagelater{tkz-base}{2020/03/03}{%
     % Package is new enough
 }{%
     \PackageError{tkz-euclide}{Package tkz-base is too old , you need a recent version}%
 }
 \makeatother
-\DeclareOption*{}%% Ne rien faire quand une option est inconnue
+\DeclareOption*{}
 \ProcessOptions
 %<----------------------------------------------------------–>
 %                          Initialisation
 %<----------------------------------------------------------–>
 \input{tkz-tools-intersections}
 \input{tkz-tools-angles}
-\usetkzobj{eu-angles,eu-arcs,eu-compass,eu-circles,eu-draw-circles,eu-lines,eu-draw-lines,eu-points,eu-points-by,eu-points-rnd,eu-points-with,eu-draw-polygons,eu-polygons,eu-protractor,eu-sectors,eu-show,eu-triangles}
+\usetkzobj{%
+   eu-angles,%
+   eu-arcs,%
+   eu-compass,%
+   eu-circles,%
+   eu-draw-circles,%
+   eu-draw-lines,%
+   eu-draw-polygons,%
+   eu-draw-triangles,%
+   eu-lines,%
+   eu-points,%
+   eu-points-by,%
+   eu-points-rnd,%
+   eu-points-with,%
+   eu-polygons,%
+   eu-protractor,%
+   eu-sectors,%
+   eu-show,%
+   eu-triangles}
 \endinput
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-angles.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-angles.tex
index bce07ea8a97..2347745e0b0 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-angles.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-angles.tex
@@ -1,11 +1,21 @@
 % tkz-tool-eu-angles.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-tool-eu-angles.tex} 
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-tool-eu-angles.tex} 
 \makeatletter
 %<--------------------------------------------------------------------------–>
 \newdimen\tkz@arcsize% from julian julian@d-and-j.net
@@ -27,8 +37,7 @@
 \endgroup  
 }
 %<--------------------------------------------------------------------------–>
-%       Mark an angle
-%<--------------------------------------------------------------------------–>
+%       Mark an angle modi 3.03 suppression de \tkz@mksize,
 %<--------------------------------------------------------------------------–>
 %                \tkzMarkAngle(B, A, C)
 %
@@ -83,7 +92,7 @@
 \tkzNormalizeAngle(\tkz@dirOne,\tkz@dirTwo)
 
 % les marques, aucune si mktype = none
-\def\tkz@mymark{\pgfsetplotmarksize{\tkz@mksize}\pgfuseplotmark{\tkz@markang}}
+\def\tkz@mymark{\pgfuseplotmark{\tkz@markang}}
 % draw the arcs
 \begin{scope}[decoration= {markings,
 	                      mark=at position \tkz@mkpos with {\tkz@mymark}}]
@@ -91,8 +100,7 @@
 		\tkzDrawArcRAN[#1,fill=none,postaction={decorate}]%
 		(#3,\tkz@size)(\tkz@FirstAngle,\tkz@SecondAngle)
   \else
-    \ifx\tkz@arc\tkz@arcdouble   
-   
+    \ifx\tkz@arc\tkz@arcdouble     
 	   \tkzDrawArcRAN[#1,fill=none](#3,\tkz@size-1.5\pgflinewidth)%
 	   				(\tkz@FirstAngle,\tkz@SecondAngle) 
        \tkzPathArcRAN[#1,fill=none,postaction={decorate}]%
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-arcs.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-arcs.tex
index c8ef72c3e6f..e58b01e25ae 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-arcs.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-arcs.tex
@@ -1,42 +1,53 @@
 % tkz-obj-eu-arcs.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-arcs.tex}  
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/23} 
+\typeout{2020/03/23 3.05c  tkz-obj-eu-arcs.tex}  
 \makeatletter
 %<------------------------------  Arcs -------------------------------------–
 % options : delta 
 % \def\tkz@delta{0}
 % \tikzset{arc style/.style={#1}}
 % \pgfkeys{/tikz/.cd,delta/.code={\def\tkz@delta{#1}}}
-
+\tikzset{arc style/.style={gray,thin}}
 \gdef\tkz@numa{0}
 \pgfkeys{/tkzdrawarc/.cd,
-			type/.is choice,
-			type/towards/.code               = \def\tkz@numa{0},
-			type/rotate/.code                = \def\tkz@numa{1},
-			type/angles/.code                = \def\tkz@numa{2}, 
-			type/R/.code                     = \def\tkz@numa{3},
-			type/R with nodes/.code          = \def\tkz@numa{4},
-			towards/.style                   = {type=towards},
-			rotate/.style                    = {type=rotate},
-			R/.style                   		   = {type=R},
-			angles/.style                    = {type=angles},
-			R with nodes/.style              = {type=R with nodes},
-			diameter/.code    				       = {},
-			arc/.code          				       = {},
-			size/.code       				         = {},
-			mark/.code          			       = {},
-			mkpos/.code        				       = {},
-			mksize/.code       				       = {},
-			mkcolor/.code       			       = {},
-			type/.default 					         =	towards,
-			delta/.store in					         = \tkz@delta,
-			delta 							             = 0,
-			/tkzdrawarc/.search also   		     = {/tikz}
+      type/.is choice,
+      type/towards/.code               = \def\tkz@numa{0},
+      type/rotate/.code                = \def\tkz@numa{1},
+      type/angles/.code                = \def\tkz@numa{2}, 
+      type/R/.code                     = \def\tkz@numa{3},
+      type/R with nodes/.code          = \def\tkz@numa{4},
+      towards/.style                   = {type=towards},
+      rotate/.style                    = {type=rotate},
+      R/.style                         = {type=R},
+      angles/.style                    = {type=angles},
+      R with nodes/.style              = {type=R with nodes},
+      diameter/.code                   = {},
+      arc/.code                        = {},
+      size/.code                       = {},
+      mark/.code                       = {},
+      mkpos/.code                      = {},
+      mksize/.code                     = {},
+      mkcolor/.code                    = {},
+      type/.default                    =  towards,
+      delta/.store in                  = \tkz@delta,
+      delta                            = 0,
+      /tkzdrawarc/.search also         = {/tikz}
 }  
 \def\tkzDrawArc{\pgfutil@ifnextchar[{\tkz@DrawArc}{\tkz@DrawArc[]}}
 \def\tkz@DrawArc[#1](#2,#3)(#4){% 
@@ -66,7 +77,7 @@
   \tkzCalcLength(#2,#3)\tkzGetLength{tkz@radius}
   \tkzFindSlopeAngle(#2,#3)\tkzGetAngle{tkz@FirstAngle}  
   \tkzFindSlopeAngle(#2,#4)\tkzGetAngle{tkz@SecondAngle}
-  \tkz@DrawArcRAngles[#1](#2,\tkz@radius pt)(\tkz@FirstAngle,\tkz@SecondAngle)  
+  \tkz@DrawArcRAngles[#1](#2,\tkz@radius pt)(\tkz@FirstAngle,\tkz@SecondAngle) 
 \endgroup
 } 
 %<--------------------------------------------------------------------------–>
@@ -78,15 +89,15 @@
                                            \tkz@DrawArcRotate[]}}  
 \def\tkz@DrawArcRotate[#1](#2,#3)(#4){%
 \begingroup
-  \tkzCalcLength(#2,#3)			\tkzGetLength{tkz@radius} 
-  \tkzFindSlopeAngle(#2,#3)		\tkzGetAngle{tkz@FirstA}
+  \tkzCalcLength(#2,#3)     \tkzGetLength{tkz@radius} 
+  \tkzFindSlopeAngle(#2,#3)   \tkzGetAngle{tkz@FirstA}
   \pgfmathadd{\tkz@FirstA}{#4}
   \edef\tkz@SecondA{\pgfmathresult}
     \pgfmathgreaterthan{#4}{0}
   \ifdim\pgfmathresult pt=1 pt\relax%
-  	\tkz@DrawArcRAngles[#1](#2,\tkz@radius pt)(\tkz@FirstA,\tkz@SecondA)
+    \tkz@DrawArcRAngles[#1](#2,\tkz@radius pt)(\tkz@FirstA,\tkz@SecondA)
   \else
-  	\tkz@DrawArcRAngles[#1](#2,\tkz@radius pt)(\tkz@SecondA,\tkz@FirstA)
+    \tkz@DrawArcRAngles[#1](#2,\tkz@radius pt)(\tkz@SecondA,\tkz@FirstA)
   \fi
   \endgroup
 }   
@@ -103,6 +114,32 @@
 \endgroup
 }   
 %<--------------------------------------------------------------------------–>
+%    Degree      #2 center #4 - #3 radius from #5 (degree) to #6(degree) 
+%<--------------------------------------------------------------------------–>
+\def\tkzDrawArcRwithNodes{\pgfutil@ifnextchar[{\tkz@DrawArcRwithNodes}{%
+                                            \tkz@DrawArcRwithNodes[]}}  
+\def\tkz@DrawArcRwithNodes[#1](#2,#3,#4)(#5,#6){%
+\begingroup
+  \tkzCalcLength(#3,#4)  
+  \tkzFindSlopeAngle(#2,#5)\tkzGetAngle{tkz@FirstAngle}  
+  \tkzFindSlopeAngle(#2,#6)\tkzGetAngle{tkz@SecondAngle}
+  \tkz@DrawArcRAngles[#1](#2,\tkzLengthResult)(\tkz@FirstAngle,\tkz@SecondAngle)
+\endgroup   
+} 
+%<--------------------------------------------------------------------------–>
+%    Nodes R  #2 center #3 radius en cm  from #4(node) to #5(node)
+%  \tkzDrawArcR(O,2 cm)(A,B)
+%<--------------------------------------------------------------------------–>
+\def\tkzDrawArcR{\pgfutil@ifnextchar[{\tkz@DrawArcR}{\tkz@DrawArcR[]}} 
+\def\tkz@DrawArcR[#1](#2,#3)(#4,#5){%
+\begingroup
+   \tkzFindSlopeAngle(#2,#4)\tkzGetAngle{tkz@FirstAngle}  
+   \tkzFindSlopeAngle(#2,#5)\tkzGetAngle{tkz@SecondAngle} 
+   \tkz@DrawArcRAngles[#1](#2,#3)(\tkz@FirstAngle,\tkz@SecondAngle)  
+\endgroup   
+}
+%<--------------------------------------------------------------------------–>
+%<--------------------------------------------------------------------------–>
 % #1 center #2 radius #4 first angle (degree) #5 second angle  (degree)  
 % angles  0 .. 180 or -180 .. 0
 %<--------------------------------------------------------------------------–>
@@ -117,51 +154,26 @@
   \ifdim\pgfmathresult pt=1 pt\relax%  
     \pgfmathgreaterthan{\tkz@FirstAngle}{\tkz@SecondAngle}
     \ifdim\pgfmathresult pt=1 pt\relax%
-     	\pgfmathsubtract{\tkz@FirstAngle}{360}
-    	\edef\tkz@FirstAngle{\pgfmathresult}%
- 	\fi 
+      \pgfmathsubtract{\tkz@FirstAngle}{360}
+      \edef\tkz@FirstAngle{\pgfmathresult}%
+  \fi 
  \else
      \pgfmathgreaterthan{\tkz@FirstAngle}{\tkz@SecondAngle}
     \ifdim\pgfmathresult pt=1 pt\relax%
-     	\pgfmathadd{\tkz@SecondAngle}{360}
-     	\edef\tkz@SecondAngle{\pgfmathresult}%
- 	\fi 
+      \pgfmathadd{\tkz@SecondAngle}{360}
+      \edef\tkz@SecondAngle{\pgfmathresult}%
+  \fi 
  \fi
  \pgfmathsubtract{\tkz@FirstAngle}{\tkz@delta}
  \edef\tkz@FirstAngle{\pgfmathresult}%
  \pgfmathadd{\tkz@SecondAngle}{\tkz@delta}
  \edef\tkz@SecondAngle{\pgfmathresult} 
-      \draw[shift = {(#2)},compass style,/tkzdrawarc/.cd,#1]%
+      \draw[shift = {(#2)},arc style,/tkzdrawarc/.cd,#1]%
        (\tkz@FirstAngle:#3) arc (\tkz@FirstAngle:\tkz@SecondAngle:#3);
 \endgroup  
 }
 %<--------------------------------------------------------------------------–>
-%    Degree      #2 center #4 - #3 radius from #5 (degree) to #6(degree) 
-%<--------------------------------------------------------------------------–>
-\def\tkzDrawArcRwithNodes{\pgfutil@ifnextchar[{\tkz@DrawArcRwithNodes}{%
-                                            \tkz@DrawArcRwithNodes[]}}  
-\def\tkz@DrawArcRwithNodes[#1](#2,#3,#4)(#5,#6){%
-\begingroup
-    \tkzCalcLength(#3,#4)  
-    \tkzFindSlopeAngle(#2,#5)\tkzGetAngle{tkz@FirstAngle}  
-    \tkzFindSlopeAngle(#2,#6)\tkzGetAngle{tkz@SecondAngle}
-    \tkz@DrawArcRAngles[#1](#2,\tkzLengthResult)%
-                            (\tkz@FirstAngle,\tkz@SecondAngle)
-\endgroup   
-} 
-%<--------------------------------------------------------------------------–>
-%    Nodes R  #2 center #3 radius en cm  from #4(node) to #5(node)
-%  \tkzDrawArcR(O,2 cm)(A,B)
-%<--------------------------------------------------------------------------–>
-\def\tkzDrawArcR{\pgfutil@ifnextchar[{\tkz@DrawArcR}{\tkz@DrawArcR[]}} 
-\def\tkz@DrawArcR[#1](#2,#3)(#4,#5){%
-\begingroup
-   \tkzFindSlopeAngle(#2,#4)\tkzGetAngle{tkz@FirstAngle}  
-   \tkzFindSlopeAngle(#2,#5)\tkzGetAngle{tkz@SecondAngle} 
-   \tkz@DrawArcRAngles[#1](#2,#3)(\tkz@FirstAngle,\tkz@SecondAngle)  
-\endgroup   
-}
-%<--------------------------------------------------------------------------–>
+
 \makeatother
 \endinput 
  
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-circles.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-circles.tex
index 9a3a726658b..901cb72348d 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-circles.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-circles.tex
@@ -1,12 +1,21 @@
 % tkz-obj-eu-circles.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
 %
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-circles.tex} 
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-circles.tex} 
 \makeatletter
 %<--------------------------------------------------------------------------–>
 %            tkzCircle center and one point 
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-compass.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-compass.tex
index dd1c46863a0..50cda7b15b5 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-compass.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-compass.tex
@@ -1,11 +1,21 @@
 % tkz-obj-eu-compass.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c tkz-obj-eu-compass.tex}  
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c tkz-obj-eu-compass.tex}  
 \makeatletter
 %<--------------------------------------------------------------------------–>
 %  Author Alain Matthes  
@@ -16,24 +26,22 @@
 %<--------------------------------------------------------------------------–>
 %                                Setup   Compass
 %<--------------------------------------------------------------------------–>
-\pgfkeys{%
-	tkzsucompass/.cd,
+\pgfkeys{tkzsucompass/.cd,
 	line width/.code   =     {\global\edef\tkz@compass@lw{#1}},
 	color/.code        =     {\global\edef\tkz@compass@color{#1}},
 	style/.code        =     {\global\edef\tkz@compass@style{#1}},
 	} 
 %<--------------------------------------------------------------------------–>
-%<--------------------------------------------------------------------------–>
-\def\tkzSetUpCompass{\pgfutil@ifnextchar[{\tkzActivOff\tkz@SetUpCompass}{%
-                                          \tkzActivOff\tkz@SetUpCompass[]}}
+\def\tkzSetUpCompass{\pgfutil@ifnextchar[{\tkz@SetUpCompass}{% remove tkzActivOff 3.03
+                                          \tkz@SetUpCompass[]}}
 %<--------------------------------------------------------------------------–>
 \def\tkz@SetUpCompass[#1]{% 
-\pgfkeys{%
-	tkzsucompass/.cd,
+\pgfkeys{tkzsucompass/.cd,
 	line width   = \tkz@euc@compasswidth,
 	color        = \tkz@euc@compasscolor,
-	style        = \tkz@euc@compassstyle
-	}  
+	style        = \tkz@euc@compassstyle,
+ /tkzsucompass/.search also   		     = {/tikz}
+}  
 \pgfqkeys{/tkzsucompass}{#1}
 \tikzset{compass style/.style={color       = \tkz@compass@color,
                                line width  = \tkz@compass@lw,
@@ -56,7 +64,7 @@
     /tkzcompass/length/.code     = {\def\tkz@length{#1}},
     /tkzcompass/ratio/.code      = {\def\tkz@ratio{#1}},  
     /tkzcompass/.unknown/.code   = {\let\searchname=\pgfkeyscurrentname
-                                 \pgfkeysalso{\searchname/.try=#1,
+                                    \pgfkeysalso{\searchname/.try=#1,
                                   /tikz/\searchname/.retry=#1}}
 }
                                         
@@ -70,15 +78,14 @@
   	ratio  = .5
   	}
 \pgfkeys{tkzcompass/.cd,#1}  
-    \tkzCalcLength(#2,#3)\tkzGetLength{tkz@tempLen}  
+\tkzCalcLength(#2,#3)\tkzGetLength{tkz@tempLen}  
 \ifnum\tkz@delta=0 %
    \pgfmathsetmacro{\tkz@delta}{min(deg(\tkz@length cm/ \tkz@tempLen pt),180)/2}
 \fi 
-    \tkzFindSlopeAngle(#2,#3)\tkzGetAngle{tkz@angle}%
-    \draw[shift ={(#2)},/tkzcompass/.cd,compass style,#1]%
-     (\tkz@angle-\tkz@delta:\tkz@tempLen pt)%
-      arc (\tkz@angle-\tkz@delta:\tkz@angle+\tkz@delta:\tkz@tempLen pt);
-           %};   
+\tkzFindSlopeAngle(#2,#3)\tkzGetAngle{tkz@angle}%
+\draw[shift ={(#2)},/tkzcompass/.cd,compass style,#1]%
+    (\tkz@angle-\tkz@delta:\tkz@tempLen pt)%
+  arc (\tkz@angle-\tkz@delta:\tkz@angle+\tkz@delta:\tkz@tempLen pt);
 \endgroup}
 %<--------------------------------------------------------------------------–> 
 \def\tkz@multiCompass#1 #2\@nil{% 
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-circles.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-circles.tex
index f8a0a055582..1b05f579afc 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-circles.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-circles.tex
@@ -1,12 +1,21 @@
 % tkz-obj-eu-draw-circles.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
 %
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-draw-circles.tex} 
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-draw-circles.tex} 
 \makeatletter 
 %for compatibility
 %<--------------------------------------------------------------------------–>
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-lines.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-lines.tex
index d837c35a1d7..3df6a484c2f 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-lines.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-lines.tex
@@ -1,11 +1,21 @@
 % tkz-obj-eu-draw-lines.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c tkz-obj-eu-draw-lines.tex}   
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c tkz-obj-eu-draw-lines.tex}   
 \makeatletter
 \def\tkz@numdl{0}
 \pgfkeys{/tkzdrawl/.cd,
@@ -225,12 +235,12 @@
    color/.code      =   {\xdef\tkz@line@color{#1}},
    style/.code      =   {\xdef\tkz@line@style{#1}},
    add/.code args   =   {#1 and #2} {\xdef\tkz@line@left{#1}%
-                                    \xdef\tkz@line@right{#2}%
-                            }
+                                    \xdef\tkz@line@right{#2}},
+       /tkzsuline/.search also={/tikz}%
 } 
 %<--------------------------------------------------------------------------–>
-\def\tkzSetUpLine{\pgfutil@ifnextchar[{\tkzActivOff\tkz@SetUpLine}{%
-                                         \tkzActivOff\tkz@SetUpLine[]}}
+\def\tkzSetUpLine{\pgfutil@ifnextchar[{\tkz@SetUpLine}{% remove tkzActivOff 3.03
+                                      \tkz@SetUpLine[]}}
 \def\tkz@SetUpLine[#1]{%
 \pgfkeys{%
       tkzsuline/.cd,
@@ -291,10 +301,10 @@
      color/.store in     = \tkz@mkcolor,
      mark/.store in      = \tkz@markseg,
      size/.store in      = \tkz@mksize,
-        size             = 4pt,
-        color            = \tkz@mk@color,
-        pos              = .5,
-        mark             = |,
+     size                = 4pt,
+     color               = \tkz@mk@color,
+     pos                 = .5,
+     mark                = |,
     /@tkzmarkoptions/.search also={/tikz},
 }
 \def\tkzMarkSegment{\pgfutil@ifnextchar[{\tkz@MarkSegment}{\tkz@MarkSegment[]}}
@@ -350,8 +360,7 @@
    \next#2\@nil
 }
 %<--------------------------------------------------------------------------–>
-\def\tkzLabelSegments{\pgfutil@ifnextchar[{\tkz@LabelSegments}{%
-                                           \tkz@LabelSegments[]}}
+\def\tkzLabelSegments{\pgfutil@ifnextchar[{\tkz@LabelSegments}{\tkz@LabelSegments[]}}
 \def\tkz@LabelSegments[#1](#2)#3{% 
 \def\tkz@optls{#1}
 \def\tkz@labelseg{#3}
@@ -363,14 +372,15 @@
 %<--------------------------------------------------------------------------–>
 %             PolySeg
 %<--------------------------------------------------------------------------–>
-\def\tkzDrawPolySeg{\pgfutil@ifnextchar[{\tkz@DrawPolySeg}{%
-                                         \tkz@DrawPolySeg[]}}
+\def\tkzDrawPolySeg{\pgfutil@ifnextchar[{\tkz@DrawPolySeg}{\tkz@DrawPolySeg[]}}
 \def\tkz@DrawPolySeg[#1](#2,#3){% 
 \begingroup
 \draw[line style,#1] (#2)
-    \foreach \po in {#3}{--(\po)};%
+     \foreach \pt in {#2,#3}{--(\pt)};%
 \endgroup
 }
+
+
 %<--------------------------------------------------------------------------–>
 %  add dim
     % \draw[dim={5cm,7pt,}]   (A) --  (B);
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-polygons.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-polygons.tex
index 6b3764ccc35..a960baa49bb 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-polygons.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-polygons.tex
@@ -1,11 +1,21 @@
 % tkz-obj-eu-polygons.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-polygons.tex} 
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-polygons.tex} 
 \makeatletter  
 %<--------------------------------------------------------------------------–>
 %                                 Polygon 
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-triangles.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-triangles.tex
new file mode 100644
index 00000000000..bc0d6b10f25
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-draw-triangles.tex
@@ -0,0 +1,66 @@
+% tkz-obj-eu-draw-triangles.tex
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+%<--------------------------------------------------------------------------–>
+%                       Draw Triangles
+%<--------------------------------------------------------------------------–>
+
+\def\tkz@numdtr{0}
+\pgfkeys{/drawtriangle/.cd,
+      equilateral/.code         = {\def\tkz@numdtr{0}},
+      half/.code                = {\def\tkz@numdtr{1}},
+      pythagore/.code           = {\def\tkz@numdtr{2}},
+      school/.code              = {\def\tkz@numdtr{3}},
+      golden/.code              = {\def\tkz@numdtr{4}},
+      sublime/.code             = {\def\tkz@numdtr{4}},
+      euclide/.code             = {\def\tkz@numdtr{5}},
+      gold/.code                = {\def\tkz@numdtr{6}},
+      cheops/.code              = {\def\tkz@numdtr{7}},
+      two angles/.code  args    = {#1 and #2}{\def\tkz@numdtr{8}%
+                                              \def\tkz@alpha{#1}%
+                                              \def\tkz@beta{#2}},
+      equilateral,
+   /drawtriangle/.search also={/tikz}
+} 
+
+\def\tkzDrawTriangle{\pgfutil@ifnextchar[{\tkz@DrawTriangle}{%
+                                         \tkz@DrawTriangle[]}}
+\def\tkz@DrawTriangle[#1](#2,#3){% 
+\begingroup
+\pgfkeys{/drawtriangle/.cd,equilateral}   
+\pgfqkeys{/drawtriangle}{#1}  
+\ifcase\tkz@numdtr%
+   \tkzDefEquilateral(#2,#3)
+\or% 1
+   \tkzDefTwoOne(#2,#3)
+\or% 2
+   \tkzDefPythagore(#2,#3)
+\or% 3
+   \tkzDefSchoolTriangle(#2,#3)
+\or% 4
+   \tkzDefGoldenTriangle(#2,#3)
+\or% 5
+   \tkzDefEuclideTriangle(#2,#3)
+\or% 6
+   \tkzDefGoldTriangle(#2,#3) 
+\or% 7
+   \tkzDefCheopsTriangle(#2,#3)  
+\or% 8
+   \tkzDefTwoAnglesTriangle(#2,#3)  
+\fi
+ \draw[/drawtriangle/.cd,line style,#1] (#2)--(#3)--(tkzPointResult)--cycle;  
+\endgroup
+}
+
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-lines.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-lines.tex
index 5246f68455a..de4323a8b0c 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-lines.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-lines.tex
@@ -1,11 +1,21 @@
 % tkz-obj-eu-lines.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c tkz-obj-eu-lines.tex}   
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c tkz-obj-eu-lines.tex}   
 \makeatletter
 %<--------------------------------------------------------------------------–>
 %                          les lignes
@@ -26,7 +36,8 @@
   K                        =  1,
   normed/.is if            =  tkz@line@normed,
   normed/.default          =  true,
-  normed                   =  false
+  normed                   =  false,
+  mediator
 } 
 
 \def\tkzDefLine{\pgfutil@ifnextchar[{\tkz@DefLine}{\tkz@DefLine[]}}
@@ -53,70 +64,86 @@
 %<--------------------------------------------------------------------------–>
 %                            tkzLineLL    revoir out !!
 %<--------------------------------------------------------------------------–>
-\def\tkzDefLineLL(#1,#2){% 
+\def\tkzDefLineLL{\pgfutil@ifnextchar[{\tkz@DefLineLL}{%
+                                         \tkz@DefLineLL[1]}} 
+\def\tkz@DefLineLL[#1](#2,#3){% 
 \begingroup
-   \pgfpointdiff{\pgfpointanchor{#1}{center}}{\pgfpointanchor{#2}{center}}%
+   \pgfpointdiff{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}%
    \pgf@xa=\pgf@x\relax%%
    \pgf@ya=\pgf@y\relax%%
    \pgfinterruptboundingbox 
-   \path[coordinate](\tkz@through)--++(\pgf@xa,\pgf@ya)%
+   \path[coordinate](\tkz@through)--++(\tkz@koeff\pgf@xa,\tkz@koeff\pgf@ya)%
          coordinate (tkzPointResult);
 	 \endpgfinterruptboundingbox
-     \iftkz@line@normed
-         \tkzVecKNorm(\tkz@through,tkzPointResult)
-     \fi
+   \iftkz@line@normed
+      \tkzVecKNorm(\tkz@through,tkzPointResult)
+   \fi
 \endgroup}% 
 %<--------------------------------------------------------------------------–>
 %                        tkzOrthLine 
 %<--------------------------------------------------------------------------–>
 \def\tkzDefOrthLine{\pgfutil@ifnextchar[{\tkz@DefOrthLine}{%
                                          \tkz@DefOrthLine[1]}} 
-\def\tkz@DefOrthLine[#1](#2,#3)(#4){% 
+\def\tkz@DefOrthLine[#1](#2,#3){% 
 \begingroup
-  \tkzVecKOrth(#2,#3)
+ \tkzDefPointWith(#2,#3) 
   \pgfnodealias{tkz@OLtmp}{tkzPointResult}
-  \tkz@VecKCoLinear[#1](#2,tkz@OLtmp,#4)
+  \tkz@VecKCoLinear[\tkz@koeff](#2,tkz@OLtmp,\tkz@through)
   \iftkz@line@normed
 	  \pgfinterruptboundingbox 
        \tkzVecKNorm(\tkz@through,tkzPointResult)
 		\endpgfinterruptboundingbox 
   \fi
-\endgroup
-} 
+\endgroup}% 
 %<--------------------------------------------------------------------------–>
 %                            tkzMediatorLine
 %<--------------------------------------------------------------------------–>
-\def\tkzDefMediatorLine(#1,#2){% new 2020 
+\def\tkzDefMediatorLine{\pgfutil@ifnextchar[{\tkz@DefMediatorLine}{%
+                                             \tkz@DefMediatorLine[1]}} 
+
+\def\tkz@DefMediatorLine[#1](#2,#3){% new 2020 
 \begingroup
-   \tkzDefEquilateral(#1,#2) 
+   \tkzDefEquilateral(#2,#3) 
    \pgfnodealias{tkzFirstPointResult}{tkzPointResult}
-	 \tkzDefEquilateral(#2,#1)
-   \pgfnodealias{tkzSecondPointResult}{tkzPointResult}
-   \iftkz@line@normed  
-   \tkzDefMidPoint(#1,#2)	
-   \pgfnodealias{tkz@mid}{tkzPointResult}
-	 \pgfinterruptboundingbox 
-   \tkzVecKNorm(tkz@mid,tkzFirstPointResult)
-   \pgfnodealias{tkzFirstPointResult}{tkzPointResult}
-   \tkzVecKNorm(tkz@mid,tkzSecondPointResult)
-   \pgfnodealias{tkzSecondPointResult}{tkzPointResult}
-	 \endpgfinterruptboundingbox 
-\fi
-\endgroup
-}
+	 \tkzDefEquilateral(#3,#2)
+   \pgfnodealias{tkzSecondPointResult}{tkzPointResult} 
+   \ifx\tkz@koeff=1 %
+   \else
+     \tkzDefMidPoint(#2,#3)
+     \pgfnodealias{tkz@mid}{tkzPointResult}
+     \tkz@VecK[\tkz@koeff](tkz@mid,tkzFirstPointResult)
+     \pgfnodealias{tkzFirstPointResult}{tkzPointResult}
+     \tkz@VecK[\tkz@koeff](tkz@mid,tkzSecondPointResult)
+     \pgfnodealias{tkzSecondPointResult}{tkzPointResult}
+   \fi
+   \iftkz@line@normed 
+      \tkzDefMidPoint(#2,#3)
+      \pgfnodealias{tkz@mid}{tkzPointResult}
+      \pgfinterruptboundingbox
+         \tkzVecKNorm[\tkz@koeff](tkz@mid,tkzFirstPointResult)
+         \pgfnodealias{tkzFirstPointResult}{tkzPointResult}
+         \tkzVecKNorm[\tkz@koeff](tkz@mid,tkzSecondPointResult)
+         \pgfnodealias{tkzSecondPointResult}{tkzPointResult}
+      \endpgfinterruptboundingbox
+   \fi
+\endgroup}
 % autre possibilité
 
 %<--------------------------------------------------------------------------–>
-%              BisectorLine   % pb avec un angle plat
+%              BisectorLine  
 %<--------------------------------------------------------------------------–>
 \def\tkzDefBisectorLine(#1,#2,#3){% 
 \begingroup
 	\pgfinterruptboundingbox 
-  \tkzDuplicateLength(#2,#1)(#2,#3)
+  \tkzDuplicateSegment(#2,#1)(#2,#3)
   \pgfnodealias{bi@tmp}{tkzPointResult}  
   \tkzDefEquilateral(bi@tmp,#1)
+  \ifx\tkz@koeff=1 %
+  \else
+    \tkzVecK[\tkz@koeff](#2,tkzPointResult)
+  \fi
   \iftkz@line@normed
-     \tkzVecKNorm(#2,tkzPointResult)
+     \tkzVecKNorm[\tkz@koeff](#2,tkzPointResult)
     \fi
 		\endpgfinterruptboundingbox 
 \endgroup
@@ -132,8 +159,12 @@
    \tkzDefMidPoint(#1,out@tmp) 
    \pgfnodealias{out@pt1}{tkzPointResult}
    \tkzURotateAngle(#2,90)(out@pt1)
+   \ifx\tkz@koeff=1 %
+   \else
+     \tkzVecK[\tkz@koeff](#2,tkzPointResult)
+   \fi
    \iftkz@line@normed
-     \tkzVecKNorm(#2,tkzPointResult)
+     \tkzVecKNorm[\tkz@koeff](#2,tkzPointResult)
     \fi
 				  \endpgfinterruptboundingbox 
 \endgroup
@@ -148,6 +179,13 @@
   \tkzDefMidPoint(#1,#3)
   \pgfnodealias{sym@pt2}{tkzPointResult}
 	\tkzUSymOrth(#2,sym@pt1)(sym@pt2)
+   \ifx\tkz@koeff=1 %
+   \else
+     \tkzVecK[\tkz@koeff](#2,tkzPointResult)
+   \fi
+  \iftkz@line@normed
+    \tkzVecKNorm[\tkz@koeff](#2,tkzPointResult)
+  \fi
 \endgroup
 }
 %<-------------------------------------------------------------------------–> 
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-by.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-by.tex
index 2ab31570ac9..6e63182107a 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-by.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-by.tex
@@ -1,11 +1,20 @@
 % tkz-tools-eu-points-by.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-tools-eu-points-by.tex}  
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-tools-eu-points-by.tex}  
 \makeatletter
 %<--------------------------------------------------------------------------–>
 %                        Transformations Géométriques
@@ -148,7 +157,9 @@ inversion/.code args={center #1 through #2}{%
                   {\pgfpointanchor{\PointCS}{center}}%
      \tkz@ax=\pgf@x%
      \tkz@ay=\pgf@y%
+      \pgfinterruptboundingbox
     \path(#1)--++(-\tkz@ax,-\tkz@ay)coordinate (\tkz@pointtsf); 
+     \endpgfinterruptboundingbox
 }       
 \endgroup 
 }
@@ -183,15 +194,16 @@ inversion/.code args={center #1 through #2}{%
 %<--------------------------------------------------------------------------–>
 \def\tkzUSymOrth(#1,#2)(#3){%
 \begingroup
-      \pgfpointdiff{\pgfpointanchor{#1}{center}}%
-                   {\pgfpointanchor{#2}{center}}%
-      \tkz@ax =\pgf@y%
-      \tkz@ay =\pgf@x%
-      \path[coordinate]%
-           (#3)--++(-\tkz@ax,\tkz@ay) coordinate  (tkz@point);
-      \tkzInterLL(#1,#2)(#3,tkz@point)
-      \pgfnodealias{tkzPointofSym}{tkzPointResult}
-      \tkz@VecK[2](#3,tkzPointofSym)
+   \pgfpointdiff{\pgfpointanchor{#1}{center}}%
+                {\pgfpointanchor{#2}{center}}%
+   \tkz@ax =\pgf@y%
+   \tkz@ay =\pgf@x%  
+   \pgfinterruptboundingbox
+   \path[coordinate] (#3)--++(-\tkz@ax,\tkz@ay) coordinate  (tkz@point);
+     \endpgfinterruptboundingbox
+   \tkzInterLL(#1,#2)(#3,tkz@point)
+   \pgfnodealias{tkzPointofSym}{tkzPointResult}
+   \tkz@VecK[2](#3,tkzPointofSym)
 \endgroup
 }
 
@@ -257,8 +269,10 @@ inversion/.code args={center #1 through #2}{%
        \pgf@xa=\pgf@x%
        \pgf@ya=\pgf@y% 
       \pgfmathparse{#2}\edef\tkz@coeff{\pgfmathresult}%
+      \pgfinterruptboundingbox
       \path[coordinate](#1)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya)%
             coordinate(\tkz@pointtsf);
+     \endpgfinterruptboundingbox
   }  
 \endgroup
 }
@@ -270,8 +284,10 @@ inversion/.code args={center #1 through #2}{%
        \pgf@xa=\pgf@x%
        \pgf@ya=\pgf@y% 
       \pgfmathparse{#2}\edef\tkz@coeff{\pgfmathresult}%
+        \pgfinterruptboundingbox
       \path[coordinate](#1)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya)%
             coordinate(tkzPointResult);
+              \endpgfinterruptboundingbox
 \endgroup
 }
 %<--------------------------------------------------------------------------–>
@@ -298,7 +314,9 @@ inversion/.code args={center #1 through #2}{%
                                  {#2}
         \tkz@bx\pgf@x%
         \tkz@by\pgf@y%
+          \pgfinterruptboundingbox
         \path[coordinate](\tkz@bx,\tkz@by)coordinate(\tkz@pointtsf);% 
+          \endpgfinterruptboundingbox
         }   
   \endgroup
 }
@@ -316,7 +334,9 @@ inversion/.code args={center #1 through #2}{%
                                  {#2}
         \tkz@bx\pgf@x%
         \tkz@by\pgf@y%
-        \path (\tkz@bx,\tkz@by) coordinate (tkzPointResult);%      
+          \pgfinterruptboundingbox
+        \path (\tkz@bx,\tkz@by) coordinate (tkzPointResult);% 
+          \endpgfinterruptboundingbox     
   \endgroup
 }   
 %<--------------------------------------------------------------------------–>
@@ -345,7 +365,9 @@ inversion/.code args={center #1 through #2}{%
                              {\tkz@Angle}
     \tkz@bx\pgf@x%
     \tkz@by\pgf@y%
-    \path[coordinate](\tkz@bx,\tkz@by)coordinate(\tkz@pointtsf);  
+      \pgfinterruptboundingbox
+    \path[coordinate](\tkz@bx,\tkz@by)coordinate(\tkz@pointtsf); 
+      \endpgfinterruptboundingbox 
 }  
 \endgroup 
 }
@@ -365,7 +387,9 @@ inversion/.code args={center #1 through #2}{%
                              {\tkz@Angle}
     \tkz@bx\pgf@x%
     \tkz@by\pgf@y%
-    \path[coordinate](\tkz@bx,\tkz@by)coordinate(tkzPointResult);  
+      \pgfinterruptboundingbox
+    \path[coordinate](\tkz@bx,\tkz@by)coordinate(tkzPointResult); 
+      \endpgfinterruptboundingbox 
 \endgroup 
 }
 %<--------------------------------------------------------------------------–>
@@ -381,16 +405,18 @@ inversion/.code args={center #1 through #2}{%
       \else
          \xdef\tkz@pointtsf{\tkz@FirstPoint}
       \fi 
-   \tkzCalcLength[cm](#1,\PointIP)\tkzGetLength{tkz@lnb}% 
-	\edef\tkz@lnc{\fpeval{1/\tkz@lnb}}
+   \tkzCalcLength[cm](#1,#2)\tkzGetLength{tkz@lna}
+   \tkzCalcLength[cm](#1,\PointIP)\tkzGetLength{tkz@lnb}
+	\edef\tkz@lnc{\tkz@lna/\tkz@lnb*\tkz@lna}
    \tkzVecKNorm[\tkz@lnb](#1,\PointIP) 
    }  
 \endgroup
 } 
 \def\tkzUInversePoint(#1,#2)(#3){%  
 \begingroup  
+   \tkzCalcLength[cm](#1,#2)\tkzGetLength{tkz@lna}% 
    \tkzCalcLength[cm](#1,#3)\tkzGetLength{tkz@lnb}% 
-    \edef\tkz@lnc{\fpeval{1/\tkz@lnb}}
+    \edef\tkz@lnc{\fpeval{\tkz@lna/\tkz@lnb*\tkz@lna}}
    \tkzVecKNorm[\tkz@lnc](#1,#3) 
 \endgroup
 } 
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-rnd.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-rnd.tex
index d11902126dd..30f20fc8b84 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-rnd.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-rnd.tex
@@ -1,13 +1,20 @@
 % tkz-obj-eu-points-rnd.tex
-% Copyright 2020 by Alain Matthes
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
 %
-% This file may be distributed and/or modified
-%
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-points-rnd.tex} 
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-points-rnd.tex} 
 %<--------------------------------------------------------------------------–>
 \makeatletter
 %<-------------------------------------------------------------------------–>
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-with.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-with.tex
index 6e235de7b3d..8d239713c7f 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-with.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points-with.tex
@@ -1,11 +1,20 @@
 % tkz-obj-eu-points-with.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-points-with.tex}   
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-points-with.tex}   
 \makeatletter
 %<--------------------------------------------------------------------------–>
 %                          Vectors
@@ -72,28 +81,33 @@
       linear/.code                = {\def\tkz@numv{2}},
       orthogonal normed/.code     = {\def\tkz@numv{3}},
       linear normed/.code         = {\def\tkz@numv{4}},
-      colinear normed/.code  args = {at#1}{\def\tkz@numv{5}\def\tkz@frompoint{#1}},
-      K/.code                     = {\pgfmathparse{#1}\def\tkz@ratio{\pgfmathresult}},
+      colinear normed/.code  args = {at #1}{\def\tkz@numv{5}\def\tkz@frompoint{#1}},
+      K/.code                     = {\edef\tkz@coeff{\fpeval{#1}}},
       K                           = 1,
+      normed/.is if               =  tkz@line@normed,
+      normed/.default             =  true,
+      normed                      =  false,
       orthogonal  
 } 
-\def\tkzDefPointWith[#1](#2,#3){%
+\def\tkzDefPointWith{\pgfutil@ifnextchar[{\tkz@DefPointWith}{\tkz@DefPointWith[]}}  
+
+\def\tkz@DefPointWith[#1](#2,#3){%
 \begingroup 
 \pgfkeys{/@pointwith/.cd,K=1}  
 \pgfqkeys{/@pointwith}{#1}
 \ifcase\tkz@numv%
  % first case 0
-   \tkz@DefVectorColinearat[\tkz@ratio](#2,#3)
+   \tkz@DefVectorColinearat[\tkz@coeff](#2,#3)
   \or% 1
-   \tkz@VecKOrth[\tkz@ratio](#2,#3)
+   \tkz@VecKOrth[\tkz@coeff](#2,#3)
   \or% 2
-   \tkz@VecK[\tkz@ratio](#2,#3)
+   \tkz@VecK[\tkz@coeff](#2,#3)
   \or% 3
-   \tkz@VecKOrthNorm[\tkz@ratio](#2,#3)
+   \tkz@VecKOrthNorm[\tkz@coeff](#2,#3)
   \or% 4
-   \tkz@VecKNorm[\tkz@ratio](#2,#3)
+   \tkz@VecKNorm[\tkz@coeff](#2,#3)
   \or% 5
-   \tkz@VecKColinearNorm[\tkz@ratio](#2,#3)
+   \tkz@VecKColinearNorm[\tkz@coeff](#2,#3)
   \fi    
 \endgroup
 } 
@@ -102,33 +116,39 @@
 %<--------------------------------------------------------------------------–>
 % tkz@numv 0
 \def\tkz@DefVectorColinearat[#1](#2,#3){%
+\iftkz@line@normed
+   \tkz@VecKColinearNorm[#1](#2,#3)
+\else
 \begingroup
   \pgfpointdiff{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}%
   \pgf@xa=\pgf@x\relax%
   \pgf@ya=\pgf@y\relax%
   \pgfinterruptboundingbox
-  \path (\tkz@frompoint)--++(\tkz@ratio\pgf@xa,\tkz@ratio\pgf@ya) coordinate (tkzPointResult);
+  \path (\tkz@frompoint)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya) coordinate (tkzPointResult);
   \endpgfinterruptboundingbox
 \endgroup
+\fi
 } 
 %<--------------------------------------------------------------------------–>
-%                   tkzVector K Orth   coeff dans #1
-%    v(AN) perp v(AB)  v(AB) v(AN) sens direct cercle trigo 
-% ||v(AN)||=||v(AB)||
+%     tkzVector K Orth   coeff dans #1
+%     v(AN) perp v(AB)  (v(AB) , v(AN) ) sens direct cercle trigo 
+%     ||v(AN)||=||v(AB)||
 %<--------------------------------------------------------------------------–>
 % tkz@numv 1
 \def\tkzVecKOrth{\pgfutil@ifnextchar[{\tkz@VecKOrth}{\tkz@VecKOrth[1]}}  
 \def\tkz@VecKOrth[#1](#2,#3){%
+\iftkz@line@normed
+   \tkz@VecKOrthNorm[#1](#2,#3)
+\else
 \begingroup
   \pgfpointdiff{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}%
   \pgf@xa=-\pgf@y%
   \pgf@ya=\pgf@x%
-  \pgfmathparse{#1}
-  \let\tkz@coeff\pgfmathresult
   \pgfinterruptboundingbox 
   \path (#2)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya) coordinate (tkzPointResult);
   \endpgfinterruptboundingbox
 \endgroup
+\fi
 }%
 
 %<--------------------------------------------------------------------------–>
@@ -138,6 +158,9 @@
 % tkz@numv 2
 \def\tkzVecK{\pgfutil@ifnextchar[{\tkz@VecK}{\tkz@VecK[1]}} 
 \def\tkz@VecK[#1](#2,#3){% 
+\iftkz@line@normed
+   \tkz@VecKNorm[#1](#2,#3)
+\else
 \begingroup 
    \pgfpointdiff{\pgfpointanchor{#2}{center}}%
                 {\pgfpointanchor{#3}{center}}%
@@ -147,8 +170,9 @@
    \let\tkz@coeff\pgfmathresult
       \pgfinterruptboundingbox 
    \path (#2)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya) coordinate (tkzPointResult);
-      \endpgfinterruptboundingbox   
+    \endpgfinterruptboundingbox   
 \endgroup
+\fi
 }% 
 %<--------------------------------------------------------------------------–>
 %              tkzVecKOrthNorm   coeff dans #1
@@ -171,7 +195,6 @@
   \endpgfinterruptboundingbox   
 \endgroup
 }%      
-
 %<--------------------------------------------------------------------------–>
 %              VectorNormalised ou K*VectorNormalised
 % A-->#2 B-->#3 N-->#4      v(AB)  devient v(AN) tq ||v(AN)||=1 si #1=1  
@@ -211,14 +234,12 @@
     \endpgfinterruptboundingbox
 \endgroup
 }%
-
 %<--------------------------------------------------------------------------–>
-%         VecKCoLinear  CN = K x AB  #1 pt #2 pt #3 pt #4 nb #5 pt result   
+%  VecKCoLinear  CN = K x AB  #1 pt #2 pt #3 pt #4 nb #5 pt result   
 % il faut modifier cette macro : on supprime #3 pour la colinéarité
 % Il suffit d'utiliser Replicate ou Duplicate     coeff dans #1
 % v(CD)=#1 x v(AB) #1 le coeff; #2-->A #3-->B #4-->C 
 %<--------------------------------------------------------------------------–>
-
 \def\tkz@VecKCoLinear[#1](#2,#3,#4){% 
 \begingroup
    \pgfpointdiff{\pgfpointanchor{#2}{center}}%
@@ -242,7 +263,6 @@
    \endpgfinterruptboundingbox                     
 \endgroup
 }% 
-
 %<-------------------------------------------------------------------------–> 
 \makeatother
 \endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex
index 774faae9219..b6d8d45318a 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex
@@ -1,11 +1,20 @@
 % tkz-obj-eu-points.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-points.tex} 
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-points.tex} 
 \makeatletter  
 %add ExCenter
 %<--------------------------------------------------------------------------–>
@@ -151,22 +160,19 @@
 %<--------------------------------------------------------------------------–>
 \def\tkzOrthoCenter(#1,#2,#3){%  H orthocentre
 \begingroup
+  \pgfinterruptboundingbox 
    \tkzUProjection(#1,#2)(#3)
    \pgfnodealias{ort@pta}{tkzPointResult}
    \tkzUProjection(#1,#3)(#2)
    \pgfnodealias{ort@ptb}{tkzPointResult}
    \tkzInterLL(#2,ort@ptb)(#3,ort@pta)
+   \endpgfinterruptboundingbox 
 \endgroup
 }
 \let\tkzDefOrthoCenter\tkzOrthoCenter
 %<--------------------------------------------------------------------------–>
-%                      GravityCenter
+%                      GravityCenter modif 3.03
 %<--------------------------------------------------------------------------–>
-% \def\tkzCentroid(#1,#2,#3){%
-% \begingroup
-%     \path[coordinate](barycentric cs:#1=1,#2=1,#3=1)coordinate (tkzPointResult);
-% \endgroup
-% }
 \def\tkzCentroid(#1,#2,#3){%
 \begingroup 
    \pgf@process{\pgfpointanchor{#1}{center}}%
@@ -184,8 +190,9 @@
    \advance\tkz@cy by\tkz@by\relax%
    \divide\tkz@cx by3\relax%
    \divide\tkz@cy by3\relax
-   \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkz@cx}{\tkz@cy}}  
-   %\path[coordinate](barycentric cs:#1=1,#2=1,#3=1)coordinate (tkzPointResult);
+   \pgfinterruptboundingbox 
+   \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkz@cx}{\tkz@cy}}
+   \endpgfinterruptboundingbox   
 \endgroup
 }
 \let\tkzBaryCenter\tkzCentroid
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-polygons.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-polygons.tex
index b9b29a666e3..d92acc32498 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-polygons.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-polygons.tex
@@ -1,11 +1,21 @@
 % tkz-obj-eu-polygons.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-polygons.tex} 
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-polygons.tex} 
+% bug in regular polygon side 2020/03/03
 \makeatletter  
 %<--------------------------------------------------------------------------–>
 %                                 Polygon 
@@ -36,10 +46,10 @@
 
 \def\tkzDefGoldRectangle(#1,#2){
 \begingroup
- 	\tkzVecKOrth[-\tkzInvPhi](#2,#1)
-    \pgfnodealias{tkzFirstPointResult}{tkzPointResult}
-  \tkzVecKOrth[\tkzInvPhi](#1,#2)
-    \pgfnodealias{tkzSecondPointResult}{tkzPointResult}
+  \tkzDefPointWith[K=-\tkzInvPhi](#2,#1)
+  \pgfnodealias{tkzFirstPointResult}{tkzPointResult}
+  \tkzDefPointWith[K=\tkzInvPhi](#1,#2)
+  \pgfnodealias{tkzSecondPointResult}{tkzPointResult}
 \endgroup
 }
 \def\tkzDrawGoldRectangle{\pgfutil@ifnextchar[{\tkz@DrawGoldRectangle}{%
@@ -50,14 +60,13 @@
 \pgfkeys{/defregpoly/.cd,
 			name/.store in    	=  \tkz@regpolname,
 			sides/.store in   	=  \tkz@regpolsides,
-			center/.code  		=  \def\tkz@numregpol{0},
-			side/.code    		=  \def\tkz@numregpol{1},
-			center,
-			name				= P,
-			sides				= 5
+			center/.code  		  =  \def\tkz@numregpol{0},
+			side/.code    	   	=  \def\tkz@numregpol{1},
+			name/.default				=  P,
+			sides/.default			=  5,
+      center
 } 
-\def\tkzDefRegPolygon{\pgfutil@ifnextchar[{\tkz@DefRegPolygon}{%
-                                         \tkz@DefRegPolygon[]}}
+\def\tkzDefRegPolygon{\pgfutil@ifnextchar[{\tkz@DefRegPolygon}{\tkz@DefRegPolygon[]}}
 \def\tkz@DefRegPolygon[#1](#2,#3){% 
 \begingroup 
 \pgfqkeys{/defregpoly}{#1}  
@@ -85,7 +94,7 @@
 \pgfmathsetmacro{\tkz@regangleside}{(180-\tkz@regangle)/2}
 \tkzDefMidPoint(#1,#2)
 \pgfnodealias{tkz@tempPt}{tkzPointResult}
-\tkzCalcLength[cm](tkz@tempPt,B) \tkzGetLength{tkz@len}
+\tkzCalcLength[cm](tkz@tempPt,#1) \tkzGetLength{tkz@len}
 \pgfmathsetmacro{\tkz@inscriberadius}{%
   \tkz@len*tan(90*(\tkz@regpolsides-2)/\tkz@regpolsides)}
 \tkzDefPointWith[orthogonal normed,K=\tkz@inscriberadius](tkz@tempPt,#2)
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-protractor.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-protractor.tex
index b1426b206c3..bfd37bc1ef0 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-protractor.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-protractor.tex
@@ -1,11 +1,20 @@
 % tkz-obj-eu-protractor.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
- \typeout{2020/01/24 3.02c tkz-obj-eu-protractor.tex}  
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+ \typeout{2020/03/03 3.05c tkz-obj-eu-protractor.tex}  
 \makeatletter
 %<--------------------------------------------------------------------------–>  
 %                   !!! idea from Y. Combe  !!! 
@@ -45,7 +54,6 @@
     \draw [>=stealth',->, thick,black] (0:2.5) arc(0:32:2.5);
     \draw [>=stealth',->, thick,black] (0:2) arc(0:32:2); 
     \draw [>=stealth',->, thick,black] (0:1.5) arc(0:32:1.5);
-\tkzActivOn
 }
 
 \def\FullProtractorReturn{%
@@ -94,8 +102,9 @@
   \tkz@@extractxy{#2}
   \global\tkz@ax\pgf@x
   \global\tkz@ay\pgf@y
-   \tkzFindSlopeAngle(#2,#3)\tkzGetAngle{cmdMO@Rap@rotate}%
-\iftkz@RappReturn
+  \tkzFindSlopeAngle(#2,#3)
+  \tkzGetAngle{cmdMO@Rap@rotate}%
+  \iftkz@RappReturn
      \global\let\tkz@@Protractor\FullProtractorReturn
  \fi
   \pgfmathsetlengthmacro{\MO@lw}{\cmdMO@Rap@lw * \cmdMO@Rap@scale}
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-sectors.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-sectors.tex
index 24fc8456736..fad5b8e70b2 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-sectors.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-sectors.tex
@@ -1,11 +1,20 @@
 % tkz-obj-eu-sectors.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-sectors.tex} 
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-sectors.tex} 
 \makeatletter  
 %<-----------------------    Sectors         ------------------------------–>
 \tikzset{sstyle/.style={#1}}
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-show.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-show.tex
index d1eb78b30e5..40a39c87e30 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-show.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-show.tex
@@ -1,11 +1,20 @@
 %tkz-obj-eu-show.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-show.tex} 
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-show.tex} 
 \makeatletter  
 %<--------------------------------------------------------------------------–>
 % finding specific points in a triangle
@@ -140,7 +149,7 @@
           gap     = -1,
           size    = 1} 
 \pgfkeys{show/.cd,#1}
-    \tkzVecKOrth(#2,#3)                
+    \tkzDefPointWith(#2,#3)               
     \pgfnodealias{tkz@OLtmp}{tkzPointResult}
     \tkz@VecKCoLinear[1](#2,tkz@OLtmp,#4)      
     \pgfnodealias{tkzPointCo}{tkzPointResult}
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-triangles.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-triangles.tex
index 5fe6b5d069f..48fa5b973f1 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-triangles.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-triangles.tex
@@ -1,11 +1,21 @@
 % tkz-obj-eu-triangles.tex
-% Copyright 2019 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c  tkz-obj-eu-triangles.tex} 
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-obj-eu-triangles.tex} 
 \makeatletter  
 %<--------------------------------------------------------------------------–>
 %                       Triangle Equilateral
@@ -36,17 +46,17 @@
 
 \def\tkzDefTwoOne(#1,#2){
 \begingroup
- \tkzVecKOrth[-.5](#2,#1)
+ \tkzDefPointWith[K=-.5](#2,#1)
  \endgroup
 }
 \def\tkzDefPythagore(#1,#2){
 \begingroup
- \tkzVecKOrth[-0.75](#2,#1) 
+ \tkzDefPointWith[K=-.75](#2,#1)
 \endgroup
 }
 \def\tkzDefSchoolTriangle(#1,#2){
 \begingroup
- \tkzVecKOrth[-1](#2,#1) 
+  \tkzDefPointWith[K=-1](#2,#1) 
  \pgfnodealias{tkz@a}{tkzPointResult}
  \tkzURotateAngle(#1,30)(#2)
  \tkzInterLL(#1,tkzPointResult)(#2,tkz@a)
@@ -65,13 +75,13 @@
 }
 \def\tkzDefGoldenTriangle(#1,#2){
 \begingroup
- \tkzVecKOrth[-\tkzInvPhi](#2,#1)
+ \tkzDefPointWith[K=-\tkzInvPhi](#2,#1)
 \endgroup
 }
 \def\tkzDefCheopsTriangle(#1,#2){
 \begingroup
-\tkzDefMidPoint(#1,#2)
- \tkzVecKOrth[-\tkzSqrtPhi](tkzPointResult,#1)
+  \tkzDefMidPoint(#1,#2)
+  \tkzDefPointWith[K=-\tkzSqrtPhi](tkzPointResult,#1)
 \endgroup
 }
 \def\tkzDefTwoAnglesTriangle(#1,#2){
@@ -127,61 +137,11 @@
   \or% 7
   \tkzDefCheopsTriangle(#2,#3)  
   \or% 8
-  \tkzDefTwoAnglesTriangle(#2,#3)  \fi    
+  \tkzDefTwoAnglesTriangle(#2,#3)  
+  \fi    
 \endgroup
 }
 %<--------------------------------------------------------------------------–>
-%                       Draw Triangles
-%<--------------------------------------------------------------------------–>
-
-\def\tkz@numdtr{0}
-\pgfkeys{/drawtriangle/.cd,
-      equilateral/.code         = {\def\tkz@numdtr{0}},
-      half/.code                = {\def\tkz@numdtr{1}},
-      pythagore/.code           = {\def\tkz@numdtr{2}},
-      school/.code              = {\def\tkz@numdtr{3}},
-      golden/.code              = {\def\tkz@numdtr{4}},
-      sublime/.code             = {\def\tkz@numdtr{4}},
-      euclide/.code             = {\def\tkz@numdtr{5}},
-      gold/.code                = {\def\tkz@numdtr{6}},
-      cheops/.code              = {\def\tkz@numdtr{7}},
-      two angles/.code  args    = {#1 and #2}{\def\tkz@numdtr{8}%
-                                              \def\tkz@alpha{#1}%
-                                              \def\tkz@beta{#2}},
-      equilateral,
-   /drawtriangle/.search also={/tikz}
-} 
-
-\def\tkzDrawTriangle{\pgfutil@ifnextchar[{\tkz@DrawTriangle}{%
-                                         \tkz@DrawTriangle[]}}
-\def\tkz@DrawTriangle[#1](#2,#3){% 
-\begingroup
-\pgfkeys{/drawtriangle/.cd,equilateral}   
-\pgfqkeys{/drawtriangle}{#1}  
-\ifcase\tkz@numdtr%
-   \tkzDefEquilateral(#2,#3)
-\or% 1
-   \tkzDefTwoOne(#2,#3)
-\or% 2
-   \tkzDefPythagore(#2,#3)
-\or% 3
-   \tkzDefSchoolTriangle(#2,#3)
-\or% 4
-   \tkzDefGoldenTriangle(#2,#3)
-\or% 5
-   \tkzDefEuclideTriangle(#2,#3)
-\or% 6
-   \tkzDefGoldTriangle(#2,#3) 
-\or% 7
-   \tkzDefCheopsTriangle(#2,#3)  
-\or% 8
-   \tkzDefTwoAnglesTriangle(#2,#3)  
-\fi
- \draw[/drawtriangle/.cd,line style,#1] (#2)--(#3)--(tkzPointResult)--cycle;  
-\endgroup
-}
-
-%<--------------------------------------------------------------------------–>
 %              les triangles sspécifiques
 %<--------------------------------------------------------------------------–>
 
@@ -250,16 +210,15 @@
 %<--------------------------------------------------------------------------–
 %<--------------------------------------------------------------------------–>
 \def\@DefIncentralTriangle(#1,#2,#3)(#4,#5){%
-   \def\tkz@tmp{#5}%
+\def\tkz@tmp{#5}%
     \tkz@recuplast(#3)
     \tkzDefBisectorLine(#2,#1,\tkz@last)
-     \tkzInterLL(#2,\tkz@last)(#1,tkzPointResult)
-     \pgfnodealias{#4}{tkzPointResult}
+    \tkzInterLL(#2,\tkz@last)(#1,tkzPointResult)
+    \pgfnodealias{#4}{tkzPointResult}
     \ifx\tkz@tmp\tkz@stop\else\@DefIncentralTriangle(#2,#3)(#5)\fi
    \pgfnodealias{\tkz@pttr@name#4}{#4}
 }
 
-
 \def\tkzDefIncentralTriangle{\pgfutil@ifnextchar[{%
                      \tkz@DefIncentralTriangle}{%
                      \tkz@DefIncentralTriangle[]}}
@@ -397,12 +356,14 @@
 \let\tkzDefMedialTriangle\tkzDefCentroidTriangle
 \let\tkzDefMidpointTriangle\tkzDefCentroidTriangle
 %<--------------------------------------------------------------------------–>
-% Orthic Triangle H Ha Hb Hc
+% Orthic Triangle H Ha Hb Hc modif 3.03
 %<--------------------------------------------------------------------------–>
 \def\@DefOrthicTriangle(#1,#2,#3)(#4,#5){%
     \def\tkz@tmp{#5}%
     \tkz@recuplast(#3)
-    \tkzUProjection(#2,\tkz@last)(#1)  
+          \pgfinterruptboundingbox 
+    \tkzUProjection(#2,\tkz@last)(#1) 
+          \endpgfinterruptboundingbox 
     \pgfnodealias{#4}{tkzPointResult}
     \ifx\tkz@tmp\tkz@stop\else\@DefOrthicTriangle(#2,#3)(#5)\fi
    \pgfnodealias{\tkz@pttr@name#4}{#4}
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-angles.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-angles.tex
index 85595fe4ca8..9a88ffeaaca 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-angles.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-angles.tex
@@ -1,11 +1,20 @@
 % tkz-tools-angles.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c tkz-tools-angles.tex}   
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c tkz-tools-angles.tex}   
 \makeatletter
 %<--------------------------------------------------------------------------–>
 %<--------------------------------------------------------------------------–>
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-intersections.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-intersections.tex
index 7bb8810796e..58a8e6e6c0e 100644
--- a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-intersections.tex
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-intersections.tex
@@ -1,11 +1,20 @@
 % tkz-tools-intersections.tex
-% Copyright 2020 by Alain Matthes
-% This file may be distributed and/or modified
-% 1. under the LaTeX Project Public License and/or
-% 2. under the GNU Public License.
-\def\fileversion{3.02c}
-\def\filedate{2020/01/24} 
-\typeout{2020/01/24 3.02c tkz-tools-intersections.tex}   
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c tkz-tools-intersections.tex}   
 \makeatletter
 %<--------------------------------------------------------------------------–>
 %                 intersection  de deux lignes
diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-math.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-math.tex
new file mode 100644
index 00000000000..97bc6c698a4
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-tools-math.tex
@@ -0,0 +1,126 @@
+% tkz-tools-math.tex
+% Copyright 2020  Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status “maintained”.
+% 
+% The Current Maintainer of this work is Alain Matthes.
+%  utf8 encoding
+\def\fileversion{3.05c}
+\def\filedate{2020/03/03} 
+\typeout{2020/03/03 3.05c  tkz-tools-math.tex}     
+\makeatletter
+%<-------------------------------------------------------------------------->
+%  \tkzpointnormalised    normalise un point A-->A' tq ||v(OA')=1||
+% équivalent de \pgfpointnormalised avec fp
+% example
+% \tkzpointnormalised{%
+% \pgfpointdiff{\pgfpointanchor{A}{center}}
+%              {\pgfpointanchor{B}{center}}}
+
+% or
+% \pgf@x=1 cm
+% \pgf@y=12 cm 
+% \tkzpointnormalised{}
+%<--------------------------------------------------------------------------
+\def\tkzpointnormalised#1{%
+\pgf@process{#1}%
+\edef\tkz@den{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}}
+\edef\tkz@coordx{\fpeval{\pgf@x/\tkz@den}}
+\edef\tkz@coordx{\fpeval{round(\tkz@coordx,5)}}
+\edef\tkz@coordy{\fpeval{\pgf@y/\tkz@den}}
+\edef\tkz@coordy{\fpeval{round(\tkz@coordy,5)}}
+\pgf@x = \tkz@coordx pt
+\pgf@y = \tkz@coordy pt
+}
+%<-------------------------------------------------------------------------->
+% restaure and save length
+\def\tkz@save@length{%
+\global\let\tkz@temp@length\tkzLengthResult}%
+\def\tkz@restore@length{%
+ \global\let\tkzLengthResult\tkz@temp@length }% 
+%<-------------------------------------------------------------------------->
+%    \tkzCalcLength      Distance entre deux points en pt ou en cm  avec xfp 
+% \veclen mais avec fp 
+%  option cm le résultat est en cm sinon en pt
+%<-------------------------------------------------------------------------->
+\pgfkeys{tkzcalclen/.cd,
+       cm/.is if         = tkzLengthIncm,
+       cm/.default       = true}   
+
+\def\tkzCalcLength{\pgfutil@ifnextchar[{\tkz@CalcLength}{\tkz@CalcLength[]}}  
+\def\tkz@CalcLength[#1](#2,#3){%
+\pgfkeys{tkzcalclen/.cd, cm = false}
+\pgfqkeys{/tkzcalclen}{#1}%   
+\begingroup
+\tkz@@CalcLength(#2,#3){tkzLengthResult}
+\iftkzLengthIncm 
+   \pgfmathparse{\tkz@xfpMathLen pt/1cm}
+	\edef\tkz@xfpMathLen{\fpeval{round(\pgfmathresult,5)}}
+   \global\let\tkzLengthResult\tkz@xfpMathLen  
+\fi 
+\endgroup
+}%
+\def\tkz@@CalcLength(#1,#2)#3{%
+\pgfpointdiff{\pgfpointanchor{#1}{center}}%
+             {\pgfpointanchor{#2}{center}}%
+\edef\tkz@xfpMathLen{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}}
+\edef\tkz@xfpMathLen{\fpeval{round(\tkz@xfpMathLen,5)}}
+\global\expandafter\edef\csname #3\endcsname{\tkz@xfpMathLen}
+}
+%<-------------------------------------------------------------------------->
+\def\tkzGetLength#1{%
+\global\expandafter\edef\csname #1\endcsname{\tkzLengthResult}}  
+%<-------------------------------------------------------------------------->
+%     \tkzpttocm  passage de pt   cm div par 28.45274
+%<-------------------------------------------------------------------------->
+\def\tkzpttocm(#1)#2{%
+\begingroup  
+  \pgfmathparse{#1/1cm}
+  \edef\tkz@mathresult{\fpeval{round(\pgfmathresult,5)}}
+  \global\let\tkz@mathresult\tkz@mathresult
+  \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}% 
+\endgroup
+}%
+%<-------------------------------------------------------------------------->
+%     \tkzcmtopt  passage de cm   pt mul par 28.45274
+%<--------------------------------------------------------------------------
+\def\tkzcmtopt(#1)#2{%
+\begingroup 
+   \pgfmathparse{#1/1pt}
+  \edef\tkz@mathresult{\fpeval{round(\pgfmathresult,5)}}
+  \global\let\tkz@mathresult\tkz@mathresult
+  \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}% 
+\endgroup  
+}% 
+%<-------------------------------------------------------------------------->
+%                          Slope
+%<-------------------------------------------------------------------------->
+\def\tkzFindSlope{\tkz@FindSlope}
+\def\tkz@FindSlope(#1,#2)#3{%
+\begingroup
+   \tkzpointnormalised{\pgfpointdiff{\pgfpointanchor{#1}{center}}%
+                                    {\pgfpointanchor{#2}{center}}}
+     \edef\tkz@Slope{\fpeval{\pgfmath@tonumber{\pgf@y}/\pgfmath@tonumber{\pgf@x}}}
+     \edef\tkz@Slope{\fpeval{round(\tkz@Slope,5)}}
+    \global\expandafter\edef\csname #3\endcsname{\tkz@Slope}%  
+\endgroup
+}
+%  Schrodinger's cat idea 03/01/20
+\tikzset{xfp/.code={%
+\pgfmathdeclarefunction*{veclen}{2}{%
+\begingroup%
+    \pgfmath@x##1pt\relax%
+    \pgfmath@y##2pt\relax%
+    \edef\tkz@xfpMathLen{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}}
+    \pgfmath@returnone\tkz@xfpMathLen pt%
+\endgroup%
+}}}
+ \makeatother 
+\endinput   
\ No newline at end of file