diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/tkz-euclide/TKZdoc-euclide-examples.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/tkz-euclide/TKZdoc-euclide-examples.tex | 204 |
1 files changed, 107 insertions, 97 deletions
diff --git a/Master/texmf-dist/doc/latex/tkz-euclide/TKZdoc-euclide-examples.tex b/Master/texmf-dist/doc/latex/tkz-euclide/TKZdoc-euclide-examples.tex index 79b340b5db6..60ecb199658 100644 --- a/Master/texmf-dist/doc/latex/tkz-euclide/TKZdoc-euclide-examples.tex +++ b/Master/texmf-dist/doc/latex/tkz-euclide/TKZdoc-euclide-examples.tex @@ -41,7 +41,7 @@ \tkzDefPointWith[orthogonal,K=-1](B,A) \tkzDrawLine[add = .5 and .5](B,tkzPointResult) \tkzInterLC[R](B,tkzPointResult)(A,8) - \tkzGetPoints{C}{J} + \tkzGetPoints{J}{C} \tkzDrawSegment(A,B) \tkzDrawPoints(A,B,C) \tkzCompass(A,C) @@ -67,7 +67,7 @@ The figure below shows a semicircle, with diameter $AB$. A tangent line is drawn \tkzDefPoint(0,0){A}\tkzDefPoint(6,0){D} \tkzDefPoint(8,0){B}\tkzDefPoint(4,0){I} \tkzDefLine[orthogonal=through D](A,D) - \tkzInterLC[R](D,tkzPointResult)(I,4) \tkzGetFirstPoint{C} + \tkzInterLC[R](D,tkzPointResult)(I,4) \tkzGetSecondPoint{C} \tkzDefLine[orthogonal=through C](I,C) \tkzGetPoint{c} \tkzDefLine[orthogonal=through B](A,B) \tkzGetPoint{b} \tkzInterLL(C,c)(B,b) \tkzGetPoint{T} @@ -201,7 +201,7 @@ The figure below shows a semicircle, with diameter $AB$. A tangent line is drawn \tkzInit[xmin=-1,xmax=11,ymin=-4,ymax=7] \tkzClip \tkzDefPoints{0/0/A,8/0/B} - \tkzDefTriangle[pythagore](A,B) + \tkzDefTriangle[pythagore,swap](A,B) \tkzGetPoint{C} \tkzDrawPolygon[fill=green!5](A,B,C) \tkzDefMidPoint(C,A) \tkzGetPoint{I} @@ -348,7 +348,7 @@ At what angle does he see these two vertices?} \tkzDefPointWith[orthogonal](I,Y) \tkzGetPoint{i} \tkzDrawLines[add = 2 and 1,color=orange](I,i) \tkzInterLL(I,i)(A,B) \tkzGetPoint{Z} - \tkzInterLC(I,i)(O,B) \tkzGetSecondPoint{M} + \tkzInterLC(I,i)(O,B) \tkzGetFirstPoint{M} \tkzDefPointWith[orthogonal](B,Z) \tkzGetPoint{b} \tkzDrawCircle(O,B) \tkzDrawLines[add = 0 and 2,color=orange](B,b) @@ -379,7 +379,7 @@ The three altitudes of a triangle intersect at the same H-point. \tkzDefPoint(5,6){A} \tkzDefMidPoint(C,B) \tkzGetPoint{I} \tkzInterLC(A,C)(I,B) - \tkzGetSecondPoint{B'} + \tkzGetFirstPoint{B'} \tkzInterLC(A,B)(I,B) \tkzGetFirstPoint{C'} \tkzInterLL(B,B')(C,C') \tkzGetPoint{H} @@ -403,8 +403,8 @@ The three altitudes of a triangle intersect at the same H-point. \tkzDefPoint(5,6){C} \tkzDefMidPoint(A,B)\tkzGetPoint{O} \tkzDefPointBy[projection=onto A--B](C) \tkzGetPoint{P} -\tkzInterLC(C,A)(O,A) -\tkzGetSecondPoint{M} +\tkzInterLC[common=A](C,A)(O,A) +\tkzGetFirstPoint{M} \tkzInterLC(C,B)(O,A) \tkzGetFirstPoint{N} \tkzInterLL(B,M)(A,N)\tkzGetPoint{I} @@ -919,8 +919,8 @@ Another solution \tkzInterLC[R](A,B)(A,1) \tkzGetPoints{D}{a2} \tkzDefMidPoint(D,E) \tkzGetPoint{I} \tkzDrawCircle[orange](I,D) -\tkzInterLC(X,H)(I,D) \tkzGetPoints{M'}{M} -\tkzInterLC(M,D)(A,D) \tkzGetPoints{P'}{P} +\tkzInterLC(X,H)(I,D) \tkzGetPoints{M}{M'} +\tkzInterLC(M,D)(A,D) \tkzGetPoints{P}{P'} \tkzInterLC(M,E)(B,E) \tkzGetPoints{Q}{Q'} \tkzInterLL(P,Q)(A,B) \tkzGetPoint{O} \tkzDrawSegments[orange](A,P I,M B,Q) @@ -931,28 +931,28 @@ Another solution \end{tikzpicture} \begin{tkzexample}[code only,small] - \begin{tikzpicture} - \tkzDefPoints{0/0/A,4/2/B,2/3/K} - \tkzDrawCircle[R](A,1)\tkzDrawCircle[R](B,3) - \tkzInterCC[R](A,1)(K,3) \tkzGetPoints{a}{a'} - \tkzInterCC[R](B,3)(K,3) \tkzGetPoints{b}{b'} - \tkzInterLL(a,a')(b,b') \tkzGetPoint{X} - \tkzDefPointBy[projection= onto A--B](X) \tkzGetPoint{H} - \tkzGetPoint{C} - \tkzInterLC[R](A,B)(B,3) \tkzGetPoints{b1}{E} - \tkzInterLC[R](A,B)(A,1) \tkzGetPoints{D}{a2} - \tkzDefMidPoint(D,E) \tkzGetPoint{I} - \tkzDrawCircle[orange](I,D) - \tkzInterLC(X,H)(I,D) \tkzGetPoints{M'}{M} - \tkzInterLC(M,D)(A,D) \tkzGetPoints{P'}{P} - \tkzInterLC(M,E)(B,E) \tkzGetPoints{Q}{Q'} - \tkzInterLL(P,Q)(A,B) \tkzGetPoint{O} - \tkzDrawSegments[orange](A,P I,M B,Q) - \tkzDrawPoints(A,B,D,E,M,I,O,P,Q,X,H) - \tkzDrawLines(O,E M,D M,E O,Q) - \tkzDrawLine[add= 3 and 4,orange](X,H) - \tkzLabelPoints(A,B,D,E,M,I,O,P,Q,X,H) - \end{tikzpicture} +\begin{tikzpicture} +\tkzDefPoints{0/0/A,4/2/B,2/3/K} +\tkzDrawCircle[R](A,1)\tkzDrawCircle[R](B,3) +\tkzInterCC[R](A,1)(K,3) \tkzGetPoints{a}{a'} +\tkzInterCC[R](B,3)(K,3) \tkzGetPoints{b}{b'} +\tkzInterLL(a,a')(b,b') \tkzGetPoint{X} +\tkzDefPointBy[projection= onto A--B](X) \tkzGetPoint{H} +\tkzGetPoint{C} +\tkzInterLC[R](A,B)(B,3) \tkzGetPoints{b1}{E} +\tkzInterLC[R](A,B)(A,1) \tkzGetPoints{D}{a2} +\tkzDefMidPoint(D,E) \tkzGetPoint{I} +\tkzDrawCircle[orange](I,D) +\tkzInterLC(X,H)(I,D) \tkzGetPoints{M}{M'} +\tkzInterLC(M,D)(A,D) \tkzGetPoints{P}{P'} +\tkzInterLC(M,E)(B,E) \tkzGetPoints{Q}{Q'} +\tkzInterLL(P,Q)(A,B) \tkzGetPoint{O} +\tkzDrawSegments[orange](A,P I,M B,Q) +\tkzDrawPoints(A,B,D,E,M,I,O,P,Q,X,H) +\tkzDrawLines(O,E M,D M,E O,Q) +\tkzDrawLine[add= 3 and 4,orange](X,H) +\tkzLabelPoints(A,B,D,E,M,I,O,P,Q,X,H) +\end{tikzpicture} \end{tkzexample} @@ -1105,10 +1105,10 @@ Since the triangles $AO_2C$ and $AO_1E$ are isosceles the angles at the base are \tkzInterCC(O,A)(M_0,B) \tkzGetFirstPoint{D} \tkzInterLL(O_1,E)(O_2,F) \tkzGetPoint{O_3} \tkzDefCircle[circum](E,F,B) \tkzGetPoint{0_4} - \tkzInterLC(A,D)(O_1,A) \tkzGetSecondPoint{I} - \tkzInterLC(C,D)(O_2,B) \tkzGetFirstPoint{K} - \tkzInterLC(A,D)(O_3,D) \tkzGetFirstPoint{G} - \tkzInterLC(C,D)(O_3,D) \tkzGetSecondPoint{H} + \tkzInterLC(A,D)(O_1,A) \tkzGetFirstPoint{I} + \tkzInterLC(C,D)(O_2,B) \tkzGetSecondPoint{K} + \tkzInterLC[common=D](A,D)(O_3,D) \tkzGetFirstPoint{G} + \tkzInterLC[common=D](C,D)(O_3,D) \tkzGetFirstPoint{H} \tkzInterLL(C,G)(B,K) \tkzGetPoint{M} \tkzInterLL(A,H)(B,I) \tkzGetPoint{L} \tkzInterLL(L,G)(A,C) \tkzGetPoint{N} @@ -1188,9 +1188,17 @@ The last example is very complex and it is to show you all that we can do with \ % !TEX TS-program = lualatex \documentclass{standalone} \usepackage{tkz-euclide} +\tkzSetUpColors[background=white,text=black] +\tkzSetUpCompass[color=orange, line width=.4pt,delta=10] +\tkzSetUpArc[color=gray,line width=.4pt] +\tkzSetUpPoint[size=2,color=teal] +\tkzSetUpLine[line width=.4pt,color=teal] +\tkzSetUpStyle[orange]{new} +\tikzset{every picture/.style={line width=.4pt}} + \begin{document} -\begin{tikzpicture}[scale=1] +\begin{tikzpicture}[scale=.75] \tkzDefPoints{0/0/A,6/0/B,0.8/4/C} % we need some special points if the triangle, tkz-euclide.sty knows about them @@ -1218,22 +1226,20 @@ The last example is very complex and it is to show you all that we can do with \ \tkzInterLL(Zc,Ya)(A,B) \tkzGetPoint{A'} \tkzDefPointBy[reflection= over Ja--Jc](C')\tkzGetPoint{Ab} \tkzDefPointBy[reflection= over Ja--Jc](A')\tkzGetPoint{Cb} - % Now we can get the center of THE CIRCLE : Q % BUT we need to find the radius or a point on the circle \tkzInterLL(K,O)(N,Sp) \tkzGetPoint{Q} -\tkzInterLC(A,B)(Q,Cb) \tkzGetSecondPoint{Ba} -\tkzInterLC(A,C)(Q,Cb) \tkzGetPoints{Ca}{Ac} -\tkzInterLC(B,C')(Q,Cb) \tkzGetSecondPoint{Bc} +\tkzInterLC(A,B)(Q,Cb) \tkzGetFirstPoint{Ba} +\tkzInterLC(A,C)(Q,Cb) \tkzGetPoints{Ac}{Ca} +\tkzInterLC(B,C')(Q,Cb) \tkzGetFirstPoint{Bc} \tkzInterLC(Q,Ja)(Q,Cb) \tkzGetSecondPoint{F'a} \tkzInterLC(Q,Jc)(Q,Cb) \tkzGetSecondPoint{F'c} \tkzInterLC(Q,Jb)(Q,Cb) \tkzGetSecondPoint{F'b} \tkzInterLC(Sp,F'a)(Ja,Za) \tkzGetFirstPoint{Fa} \tkzInterLC(Sp,F'b)(Jb,Yb) \tkzGetFirstPoint{Fb} -\tkzInterLC(Sp,F'c)(Jc,Yc) \tkzGetSecondPoint{Fc} -\tkzInterLC(Mc,Sp)(Q,Cb) \tkzGetSecondPoint{A''} +\tkzInterLC(Sp,F'c)(Jc,Yc) \tkzGetFirstPoint{Fc} +\tkzInterLC(Mc,Sp)(Q,Cb) \tkzGetFirstPoint{A''} \tkzDefLine[parallel=through A''](N,Mc) \tkzGetPoint{q} - % Calculations are done, now you can draw, mark and label \tkzDrawPolygon(A,B,C) \tkzDrawCircle(Q,Bc)% @@ -1262,66 +1268,70 @@ The last example is very complex and it is to show you all that we can do with \ \tkzMarkRightAngles(Jc,Zc,A Ja,Xa,B Jb,Yb,C) \tkzDrawSegments[green,dashed](A,F'a B,F'b C,F'c) \end{tikzpicture} - \end{document} \end{tkzexample} \subsubsection*{The result} % \begin{tikzpicture}[scale=.6] - \tkzDefPoints{0/0/A,6/0/B,0.8/4/C} - \tkzDefTriangleCenter[euler](A,B,C) \tkzGetPoint{N} - \tkzDefTriangleCenter[circum](A,B,C) \tkzGetPoint{O} - \tkzDefTriangleCenter[lemoine](A,B,C) \tkzGetPoint{K} - \tkzDefTriangleCenter[ortho](A,B,C) \tkzGetPoint{H} - \tkzDefSpcTriangle[excentral,name=J](A,B,C){a,b,c} - \tkzDefSpcTriangle[centroid,name=M](A,B,C){a,b,c} - \tkzDefCircle[in](Ma,Mb,Mc) \tkzGetPoint{Sp} % Sp Spieker center - \tkzDefProjExcenter[name=J](A,B,C)(a,b,c){Y,Z,X} - \tkzDefLine[parallel=through Za](A,B) \tkzGetPoint{Xc} - \tkzInterLL(Za,Xc)(C,B) \tkzGetPoint{C'} - \tkzDefLine[parallel=through Zc](B,C) \tkzGetPoint{Ya} - \tkzInterLL(Zc,Ya)(A,B) \tkzGetPoint{A'} - \tkzDefPointBy[reflection= over Ja--Jc](C')\tkzGetPoint{Ab} - \tkzDefPointBy[reflection= over Ja--Jc](A')\tkzGetPoint{Cb} - \tkzInterLL(K,O)(N,Sp) \tkzGetPoint{Q} - \tkzInterLC(A,B)(Q,Cb) \tkzGetSecondPoint{Ba} - \tkzInterLC(A,C)(Q,Cb) \tkzGetPoints{Ca}{Ac} - \tkzInterLC(B,C')(Q,Cb) \tkzGetSecondPoint{Bc} - \tkzInterLC(Q,Ja)(Q,Cb) \tkzGetSecondPoint{F'a} - \tkzInterLC(Q,Jc)(Q,Cb) \tkzGetSecondPoint{F'c} - \tkzInterLC(Q,Jb)(Q,Cb) \tkzGetSecondPoint{F'b} - \tkzInterLC(Sp,F'a)(Ja,Za) \tkzGetFirstPoint{Fa} - \tkzInterLC(Sp,F'b)(Jb,Yb) \tkzGetFirstPoint{Fb} - \tkzInterLC(Sp,F'c)(Jc,Yc) \tkzGetSecondPoint{Fc} - \tkzInterLC(Mc,Sp)(Q,Cb) \tkzGetSecondPoint{A''} - \tkzDefLine[parallel=through A''](N,Mc) \tkzGetPoint{q} - \tkzDrawPolygon(A,B,C) - \tkzDrawCircle(Q,Bc)% - \tkzDrawCircle[euler,lightgray](A,B,C) - \tkzDrawCircles[ex](A,B,C B,C,A C,A,B) - \tkzDrawSegments[dashed](A,A' C,C' A',Zc Za,C' B,Cb B,Ab A,Ca C,Ac Ja,Xa Jb,Yb Jc,Zc) - \begin{scope} - \tkzClipCircle(Q,Cb) - \tkzDrawLine[add=5 and 12,orange](K,O) - \tkzDrawLine[add=12 and 28,red!50!black](N,Sp) - \end{scope} - \tkzDrawSegments[color=green!50!black](Mc,N Mc,A'' A'',Q) - \tkzDrawSegments[color=red,dashed](Ac,Ab Ca,Cb Ba,Bc Ja,Jc A',Cb C',Ab) - \tkzDrawSegments[color=red](Cb,Ab Bc,Ac Ba,Ca A',C') - \tkzMarkSegments[color=red,mark=|](Cb,Ab Bc,Ac Ba,Ca) - \tkzMarkRightAngles(Jc,Zc,A Ja,Xa,B Jb,Yb,C) - \tkzDrawSegments[green,dashed](A,F'a B,F'b C,F'c) - \tkzDrawPoints(A,B,C,K,Ja,Jb,Jc,Q,N,O,Sp,Mc,Xa,Xb,Yb,Yc,Za,Zc, - A',C',A'',Ab,Cb,Bc,Ca,Ac,Ba,Fa,Fb,Fc,F'a,F'b,F'c) - \tkzLabelPoints(Ja,Jb,Jc,Q,Xa,Xb,Za,Zc,Ab,Cb, - Bc, Ca, Ac, Ba, F'b) - \tkzLabelPoints[above](O, K, F'a, Fa, A'') - \tkzLabelPoints[below](B, F'c, Yc, N, Sp, Fc, Mc) - \tkzLabelPoints[left](A', C', Fb) - \tkzLabelPoints[right](C) - \tkzLabelPoints[below right](A) - \tkzLabelPoints[above right](Yb) +\tkzDefPoints{0/0/A,6/0/B,0.8/4/C} +\tkzDefTriangleCenter[euler](A,B,C) \tkzGetPoint{N} +\tkzDefTriangleCenter[circum](A,B,C) \tkzGetPoint{O} +\tkzDefTriangleCenter[lemoine](A,B,C) \tkzGetPoint{K} +\tkzDefTriangleCenter[ortho](A,B,C) \tkzGetPoint{H} +\tkzDefSpcTriangle[excentral,name=J](A,B,C){a,b,c} +\tkzDefSpcTriangle[centroid,name=M](A,B,C){a,b,c} +\tkzDefCircle[in](Ma,Mb,Mc) \tkzGetPoint{Sp} + +\tkzDefProjExcenter[name=J](A,B,C)(a,b,c){Y,Z,X} +\tkzDefLine[parallel=through Za](A,B) \tkzGetPoint{Xc} +\tkzInterLL(Za,Xc)(C,B) \tkzGetPoint{C'} +\tkzDefLine[parallel=through Zc](B,C) \tkzGetPoint{Ya} +\tkzInterLL(Zc,Ya)(A,B) \tkzGetPoint{A'} +\tkzDefPointBy[reflection= over Ja--Jc](C')\tkzGetPoint{Ab} +\tkzDefPointBy[reflection= over Ja--Jc](A')\tkzGetPoint{Cb} + +\tkzInterLL(K,O)(N,Sp) \tkzGetPoint{Q} +\tkzInterLC(A,B)(Q,Cb) \tkzGetFirstPoint{Ba} +\tkzInterLC(A,C)(Q,Cb) \tkzGetPoints{Ac}{Ca} +\tkzInterLC(B,C')(Q,Cb) \tkzGetFirstPoint{Bc} +\tkzInterLC(Q,Ja)(Q,Cb) \tkzGetSecondPoint{F'a} +\tkzInterLC(Q,Jc)(Q,Cb) \tkzGetSecondPoint{F'c} +\tkzInterLC(Q,Jb)(Q,Cb) \tkzGetSecondPoint{F'b} +\tkzInterLC(Sp,F'a)(Ja,Za) \tkzGetFirstPoint{Fa} +\tkzInterLC(Sp,F'b)(Jb,Yb) \tkzGetFirstPoint{Fb} +\tkzInterLC(Sp,F'c)(Jc,Yc) \tkzGetFirstPoint{Fc} +\tkzInterLC(Mc,Sp)(Q,Cb) \tkzGetFirstPoint{A''} +\tkzDefLine[parallel=through A''](N,Mc) \tkzGetPoint{q} +\tkzDrawPolygon(A,B,C) +\tkzDrawCircle(Q,Bc)% +\tkzDrawCircle[euler,lightgray](A,B,C) +\tkzDrawCircles[ex](A,B,C B,C,A C,A,B) +\tkzDrawSegments[dashed](A,A' C,C' A',Zc Za,C' B,Cb B,Ab A,Ca C,Ac + Ja,Xa Jb,Yb Jc,Zc) + +\begin{scope} + \tkzClipCircle(Q,Cb) + \tkzDrawLine[add=5 and 12,orange](K,O) + \tkzDrawLine[add=12 and 28,red!50!black](N,Sp) +\end{scope} + +\tkzDrawPoints(A,B,C,K,Ja,Jb,Jc,Q,N,O,Sp,Mc,Xa,Xb,Yb,Yc,Za,Zc) +\tkzDrawPoints(A',C',A'',Ab,Cb,Bc,Ca,Ac,Ba,Fa,Fb,Fc,F'a,F'b,F'c) +\tkzLabelPoints(Ja,Jb,Jc,Q,Xa,Xb,Za,Zc,Ab,Cb,Bc,Ca,Ac,Ba,F'b) +\tkzLabelPoints[above](O,K,F'a,Fa,A'') +\tkzLabelPoints[below](B,F'c,Yc,N,Sp,Fc,Mc) +\tkzLabelPoints[left](A',C',Fb) +\tkzLabelPoints[right](C) +\tkzLabelPoints[below right](A) +\tkzLabelPoints[above right](Yb) +\tkzDrawSegments[color=green!50!black](Mc,N Mc,A'' A'',Q) +\tkzDrawSegments[color=red,dashed](Ac,Ab Ca,Cb Ba,Bc Ja,Jc A',Cb C',Ab) +\tkzDrawSegments[color=red](Cb,Ab Bc,Ac Ba,Ca A',C') +\tkzMarkSegments[color=red,mark=|](Cb,Ab Bc,Ac Ba,Ca) +\tkzMarkRightAngles(Jc,Zc,A Ja,Xa,B Jb,Yb,C) +\tkzDrawSegments[green,dashed](A,F'a B,F'b C,F'c) \end{tikzpicture} + \endinput
\ No newline at end of file |