Codes Tikz des figures
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Figure 0
\documentclass[10pt, margin=2mm, tikz]{standalone} \usepackage{fourier,calc,tkz-euclide} \tkzSetUpColors[background=white,text=black] \tkzSetUpCompass[color=orange, line width=.2pt,delta=10] \tkzSetUpArc[color=gray,line width=.2pt] \tkzSetUpPoint[size=2,color=teal] \tkzSetUpLine[line width=.2pt,color=teal] \tkzSetUpStyle[color=orange,line width=.2pt]{new} \tikzset{every picture/.style={line width=.2pt}} \tikzset{label angle style/.append style={color=teal,font=\footnotesize}} \tikzset{label style/.append style={below,color=teal,font=\scriptsize}} \tikzset{new/.style={color=orange,line width=.2pt}} \begin{document} \begin{tikzpicture}[scale=1,label style/.style={font=\tiny}] \tkzDefPoint(.5,0){O} \tkzDefPoint(2,2){A} \tkzCalcLength(O,A) \tkzGetLength{rAC} \tkzDefCircle[R](O,\rAC) \tkzDrawCircle[thin,teal](O,A) \tkzDefPointOnCircle[through = center O angle 90 point A] \tkzGetPoint{B} \tkzDefPointOnCircle[through = center O angle 150 point A] \tkzGetPoint{C} \tkzDefPointOnCircle[through = center O angle 210 point A] \tkzGetPoint{D} \tkzDefPointOnCircle[through = center O angle -45 point A] \tkzGetPoint{E} \tkzFillAngle[fill=blue!30, opacity=0.5](D,O,E) \tkzFillAngle[fill=red!30, opacity=0.5](D,B,E) \tkzFillAngle[fill=red!30, opacity=0.5](D,C,E) \tkzFillAngle[fill=red!30, opacity=0.5](D,A,E) \tkzLabelAngle[blue,pos=.5](D,O,E){\tiny $2\alpha$} \tkzLabelAngle[red,pos=.5](D,B,E){\tiny $\alpha$} \tkzLabelAngle[red,pos=.5](D,C,E){\tiny $\alpha$} \tkzLabelAngle[red,pos=.5](D,A,E){\tiny $\alpha$} \tkzMarkAngle[gray,stealth-stealth,size=1](D,O,E) \tkzMarkAngle[gray,stealth-stealth,size=1](D,B,E) \tkzMarkAngle[gray,stealth-stealth,size=1](D,C,E) \tkzMarkAngle[gray,stealth-stealth,size=1](D,A,E) \tkzDrawSegments[thin](D,O O,E) \tkzDrawSegments[thin](D,B B,E) \tkzDrawSegments[thin](D,C C,E) \tkzDrawSegments[thin](D,A A,E) \tkzDrawArc[thick,teal!80!black,delta=0](O,D)(E) %\tkzLabelSegment[above left](C,A){$2\sqrt{2}$} \tkzDrawPoints(O,A,B,C,D,E) \tkzLabelPoints[teal!50!black,above](O)%,A,B,C,D,E) \end{tikzpicture} \end{document}
Figure 1
\documentclass[10pt, margin=2mm, tikz]{standalone} \usepackage{fourier,calc,tkz-euclide} \tkzSetUpColors[background=white,text=black] \tkzSetUpCompass[color=orange, line width=.2pt,delta=10] \tkzSetUpArc[color=gray,line width=.2pt] \tkzSetUpPoint[size=2,color=teal] \tkzSetUpLine[line width=.2pt,color=teal] \tkzSetUpStyle[color=orange,line width=.2pt]{new} \tikzset{every picture/.style={line width=.2pt}} \tikzset{label angle style/.append style={color=teal,font=\footnotesize}} \tikzset{label style/.append style={below,color=teal,font=\scriptsize}} \tikzset{new/.style={color=orange,line width=.2pt}} \begin{document} \begin{tikzpicture}[scale=.75] \tkzDefPoint(0,0){O} \tkzDefPointOnCircle[R = center O angle -90 radius 2] \tkzGetPoint{A} \tkzDrawSegment(O,A) \tkzDrawCircle(O,A) \tkzDefLine[tangent at=A](O) \tkzGetPoint{h} \tkzDrawLine[add = 2 and 3](A,h) \tkzDefPointOnLine[pos=2](A,h)\tkzGetPoint{C} \tkzDefPointOnLine[pos=3](A,h)\tkzGetPoint{D} \tkzDefPointOnLine[pos=-1](A,h)\tkzGetPoint{E} \tkzDefPointOnCircle[through = center O angle 30 point A] \tkzGetPoint{B} \tkzDefPointOnCircle[through = center O angle 190 point A] \tkzGetPoint{P} \tkzDrawSegments[thin](A,B B,P P,A) \tkzFillAngle[fill=red!30, opacity=0.5](A,P,B) \tkzMarkAngle[gray,stealth-stealth,size=1](A,P,B) \tkzFillAngle[fill=red!30, opacity=0.5](C,A,B) \tkzMarkAngle[gray,stealth-stealth,size=1](C,A,B) %------ \tkzMarkRightAngle[size=.2](O,A,E) \tkzDrawPoints(O,A,B,C,P) \tkzLabelPoints[teal!70!black,below](A,C) \tkzLabelPoints[teal!70!black,left](P) \tkzLabelPoints[teal!70!black,right](O,B) \tkzLabelPoint[above,font=\tiny](D){tangente} \end{tikzpicture} \end{document}
Figure 2
\documentclass[10pt, margin=2mm, tikz]{standalone} \usepackage{fourier,calc,tkz-euclide} \tkzSetUpColors[background=white,text=black] \tkzSetUpCompass[color=orange, line width=.2pt,delta=10] \tkzSetUpArc[color=gray,line width=.2pt] \tkzSetUpPoint[size=2,color=teal] \tkzSetUpLine[line width=.2pt,color=teal] \tkzSetUpStyle[color=orange,line width=.2pt]{new} \tikzset{every picture/.style={line width=.2pt}} \tikzset{label angle style/.append style={color=teal,font=\footnotesize}} \tikzset{label style/.append style={below,color=teal,font=\scriptsize}} \tikzset{new/.style={color=orange,line width=.2pt}} \begin{document} \begin{tikzpicture}[scale=.75] \tkzDefPoint(0,0){O} \tkzDefPointOnCircle[R = center O angle -90 radius 2] \tkzGetPoint{A} \tkzDrawSegment(O,A) \tkzDrawCircle(O,A) \tkzDefLine[tangent at=A](O) \tkzGetPoint{h} \tkzDrawLine[add = 2 and 3](A,h) \tkzDefPointOnLine[pos=2](A,h)\tkzGetPoint{C} \tkzDefPointOnLine[pos=3](A,h)\tkzGetPoint{D} \tkzDefPointOnLine[pos=-1](A,h)\tkzGetPoint{E} \tkzDefPointOnCircle[through = center O angle 30 point A] \tkzGetPoint{B} \tkzDrawSegments[thin](A,B O,A O,B) \tkzFillAngle[fill=red!30, opacity=0.5, size=.8](A,O,B) \tkzMarkAngle[gray,stealth-stealth,size=.8](A,O,B) \tkzLabelAngle[red,font=\tiny,pos=.5](A,O,B){$2\alpha$} \tkzFillAngle[fill=red!30, opacity=0.5, size=.8](C,A,B) \tkzMarkAngle[gray,stealth-stealth,size=.8](C,A,B) \tkzLabelAngle[red,font=\tiny,pos=.5](C,A,B){$\alpha$} %------ \tkzMarkRightAngle[size=.2](O,A,E) \tkzDrawPoints(O,A,B,C) \tkzLabelPoints[teal!70!black,below](A,C) \tkzLabelPoints[teal!70!black,left](O) \tkzLabelPoints[teal!70!black,right](B) \tkzLabelPoint[above,font=\tiny](D){tangente} \end{tikzpicture} \end{document}
Figure 3
\documentclass[10pt, margin=2mm, tikz]{standalone} \usepackage{fourier,calc,tkz-euclide} \tkzSetUpColors[background=white,text=black] \tkzSetUpCompass[color=orange, line width=.2pt,delta=10] \tkzSetUpArc[color=gray,line width=.2pt] \tkzSetUpPoint[size=2,color=teal] \tkzSetUpLine[line width=.2pt,color=teal] \tkzSetUpStyle[color=orange,line width=.2pt]{new} \tikzset{every picture/.style={line width=.2pt}} \tikzset{label angle style/.append style={color=teal,font=\footnotesize}} \tikzset{label style/.append style={below,color=teal,font=\scriptsize}} \tikzset{new/.style={color=orange,line width=.2pt}} \begin{document} \begin{tikzpicture}[scale=.75] \tkzDefPoint(0,0){O} \tkzDefPointOnCircle[R = center O angle -90 radius 2] \tkzGetPoint{A} \tkzDrawSegment(O,A) \tkzDrawCircle(O,A) \tkzDefLine[tangent at=A](O) \tkzGetPoint{h} \tkzDrawLine[add = 2 and 3](A,h) \tkzDefPointOnLine[pos=-1.5](A,h)\tkzGetPoint{C} \tkzDefPointOnLine[pos=3](A,h)\tkzGetPoint{D} \tkzDefPointOnLine[pos=-1](A,h)\tkzGetPoint{E} \tkzDefPointOnCircle[through = center O angle 30 point A] \tkzGetPoint{B} %\tkzDefPointOnCircle[through = center O angle 190 point A] \tkzGetPoint{P} \tkzDrawSegments[thin](A,B O,A O,B) \tkzFillAngle[fill=red!30, opacity=0.5, size=.8](B,O,A) \tkzMarkAngle[gray,stealth-stealth,size=.8](B,O,A) \tkzLabelAngle[red,font=\tiny,pos=.5](B,O,A){$2\alpha$} \tkzFillAngle[fill=red!30, opacity=0.5, size=.8](B,A,C) \tkzMarkAngle[gray,stealth-stealth,size=.8](B,A,C) \tkzLabelAngle[red,font=\tiny,pos=.5](B,A,C){$\alpha$} %------ \tkzMarkRightAngle[size=.2](O,A,E) \tkzDrawPoints(O,A,B,C) \tkzLabelPoints[teal!70!black,below](A,C) \tkzLabelPoints[teal!70!black,left](O) \tkzLabelPoints[teal!70!black,right](B) \tkzLabelPoint[above,font=\tiny](D){tangente} \end{tikzpicture} \end{document}
Figure 4
\documentclass[10pt, margin=2mm, tikz]{standalone} \usepackage{fourier,calc,tkz-euclide} \tkzSetUpColors[background=white,text=black] \tkzSetUpCompass[color=orange, line width=.2pt,delta=10] \tkzSetUpArc[color=gray,line width=.2pt] \tkzSetUpPoint[size=2,color=teal] \tkzSetUpLine[line width=.2pt,color=teal] \tkzSetUpStyle[color=orange,line width=.2pt]{new} \tikzset{every picture/.style={line width=.2pt}} \tikzset{label angle style/.append style={color=teal,font=\footnotesize}} \tikzset{label style/.append style={below,color=teal,font=\scriptsize}} \tikzset{new/.style={color=orange,line width=.2pt}} \begin{document} \begin{tikzpicture}[scale=.75] \tkzDefPoint(0,0){O} \tkzDefPointOnCircle[R = center O angle -90 radius 2] \tkzGetPoint{A} \tkzDrawSegment(O,A) \tkzDrawCircle(O,A) \tkzDefLine[tangent at=A](O) \tkzGetPoint{h} \tkzDefPointOnCircle[through = center O angle 30 point A] \tkzGetPoint{B} \tkzDefLine[tangent at=B](O) \tkzGetPoint{i} \tkzDrawLine[add = 2 and 3](A,h) \tkzDrawLine[add = 4 and 1](B,i) \tkzDefPointOnLine[pos=1](B,i)\tkzGetPoint{D} \tkzDefPointOnLine[pos=-1](A,h)\tkzGetPoint{E} \tkzInterLL(B,D)(A,E) \tkzGetPoint{P} \tkzDrawSegments[thin](O,A O,B) \tkzDrawSegments[thick](P,A P,B) %------ \tkzMarkRightAngle[size=.2](O,A,E) \tkzMarkRightAngle[size=.2](D,B,O) \tkzDrawPoints(O,A,B,P) \tkzLabelPoints[teal!70!black,below](A,P) \tkzLabelPoints[teal!70!black,left](O) \tkzLabelPoints[teal!70!black,right](B) %\tkzLabelPoint[above,font=\tiny](D){tangente} \end{tikzpicture} \end{document}
Figure 5
\documentclass[10pt, margin=2mm, tikz]{standalone} \usepackage{fourier,calc,tkz-euclide} \tkzSetUpColors[background=white,text=black] \tkzSetUpCompass[color=orange, line width=.2pt,delta=10] \tkzSetUpArc[color=gray,line width=.2pt] \tkzSetUpPoint[size=2,color=teal] \tkzSetUpLine[line width=.2pt,color=teal] \tkzSetUpStyle[color=orange,line width=.2pt]{new} \tikzset{every picture/.style={line width=.2pt}} \tikzset{label angle style/.append style={color=teal,font=\footnotesize}} \tikzset{label style/.append style={below,color=teal,font=\scriptsize}} \tikzset{new/.style={color=orange,line width=.2pt}} \begin{document} \begin{tikzpicture}[scale=.75] \tkzDefPoint(0,0){O} \tkzDefPointOnCircle[R = center O angle -90 radius 2] \tkzGetPoint{C} \tkzDrawSegment(O,C) \tkzDrawCircle(O,C) \tkzDefLine[tangent at=C](O) \tkzGetPoint{h} \tkzDefPointOnLine[pos=-1](C,h)\tkzGetPoint{E} \tkzDefPointOnCircle[through = center O angle -15 point C] \tkzGetPoint{A} \tkzDefPointOnCircle[through = center O angle 120 point C] \tkzGetPoint{B} \tkzDrawLine[add = 1 and .5](A,B) \tkzDrawLine[add = 2 and 4](C,h) \tkzInterLL(A,B)(C,h) \tkzGetPoint{P} \tkzDrawSegments[very thick](P,C P,B) %------ \tkzMarkRightAngle[size=.2](O,C,E) \tkzDrawPoints(O,A,B,C,P) \tkzLabelPoints[teal!70!black,above](B) \tkzLabelPoints[teal!70!black,below](C,P) \tkzLabelPoints[teal!70!black,left](O) \tkzLabelPoints[teal!70!black,above right](A) %\tkzLabelPoint[above,font=\tiny](D){tangente} \end{tikzpicture} \end{document}
Figures 6a à 6c
\documentclass{standalone} \usepackage{tkz-euclide} \usetikzlibrary{decorations.pathreplacing,calc} % Configuration globale \tkzSetUpColors[background=white,text=black] \tkzSetUpCompass[color=orange, line width=.2pt,delta=10] \tkzSetUpArc[color=gray,line width=.2pt] \tkzSetUpPoint[size=2,color=teal] \tkzSetUpLine[line width=.6pt,color=teal] %\tkzSetUpStyle[color=orange,line width=.2pt]{new} \tikzset{every picture/.style={line width=.2pt}} \tikzset{label angle style/.append style={color=teal,font=\footnotesize}} \tikzset{label style/.append style={below,color=teal,font=\scriptsize}} \tikzset{new/.style={color=orange,line width=.8pt}} \tikzset{ label style/.append style={font=\tiny, color=teal}, % Style des étiquettes des points point style/.style={circle, draw=teal, fill=teal!20!white, inner sep=.5pt} % Style des points eux-mêmes } \begin{document} \begin{tikzpicture}[framed,scale=.5] % Initialisation du plan \tkzInit[xmin=-6,xmax=6,ymin=-4,ymax=4] \tkzClip[space=0.3] % Points de base \tkzDefPoint(-4,0){M} \tkzDefPoint(4,0){N} \tkzDefMidPoint(M,N)\tkzGetPoint{O} % Cercle \tkzDrawCircle[thick](O,N) % Droites \tkzDefPoint(-6,-3){a} \tkzDefPoint(6,0){b} \tkzDefPoint(-6,3){c} \tkzDefPoint(6,-4){d} \tkzDrawLines(a,b c,d) % Intersections avec le cercle \tkzInterLC(a,b)(O,N)\tkzGetPoints{A}{B} \tkzInterLC(c,d)(O,N)\tkzGetPoints{C}{D} % Intersection des droites \tkzInterLL(a,b)(c,d)\tkzGetPoint{E} % Points et étiquettes \tkzLabelPoints[above](C,E) \tkzLabelPoints[below right](B) \tkzLabelPoints[below](A,D) % Segments colorés \tkzDrawSegment[new](B,E) \tkzDrawSegment[new](E,A) \tkzDrawSegment[new](D,E) \tkzDrawSegment[new](E,C) % Diagonales en pointillés \tkzDrawSegments[style=dashed](A,D B,C) \tkzDrawPoints(A,B,C,D,E)%,M,N,O) % à decommenter pour suite construction % \tkzFillAngle[fill=red!30, opacity=0.5, size=.8](A,E,D) % \tkzFillAngle[fill=red!30, opacity=0.5, size=.8](B,E,C) % à decommenter pour suite construction % \tkzFillAngle[fill=red!30, opacity=0.5, size=1.5](E,D,A) % \tkzFillAngle[fill=red!30, opacity=0.5, size=1.5](C,B,E) % \tkzDrawArc[line width=3pt,color=red!30,delta=0](O,C)(A) % à decommenter pour suite construction \tkzFillPolygon[red!60,opacity=0.45](A,D,E) \tkzFillPolygon[red!60,opacity=0.45](B,C,E) \end{tikzpicture} \end{document}