126 lines
4.9 KiB
TeX
Executable File
126 lines
4.9 KiB
TeX
Executable File
\documentclass{standalone}
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%
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\usepackage{tikz}
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%
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\usepackage{tkz-euclide}
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\usetkzobj{all}
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%
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\usepackage{dsfont}
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%
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\usepackage{xcolor}
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%
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\definecolor{space}{HTML}{1F2C4E}
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\definecolor{earth}{HTML}{0089FA}
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\definecolor{dida}{HTML}{FFDE00}
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\definecolor{title}{HTML}{FBA706}
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%
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\usepackage{amsmath}
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%
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\usepackage{fontspec}
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\setmainfont{Open Dyslexic}
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%
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\title{Un fatto curioso sui semicerchi}
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\begin{document}
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\begin{tikzpicture}
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\draw [use as bounding box,color=white] (-0.2,15.2) -| (30.2,15.2) |- (30.2,-60) -| (-0.2,-60);
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%title
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\draw [black,ultra thick,fill=title] (0,7) rectangle (30,15);
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\node (example-textwidth-2) [right, align=center, text width=30cm, color=black, font=\fontsize{90pt}{91pt}\selectfont] at (0,11) {Un fatto curioso sui semicerchi};
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\def\a{5}
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\def\b{9}
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\begin{scope}[shift={(0,4)}]
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\tkzDefPoint(15,0){C1}
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\tkzDefShiftPoint[C1](\a,0){A}
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\tkzDefShiftPoint[C1](-\a,0){A1}
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\tkzDefShiftPoint[C1](0,-\a-\b){C2}
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\tkzDefShiftPoint[C2](\b,0){B}
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\tkzDefShiftPoint[C2](-\b,0){B1}
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%
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\tkzDrawSector[rotate,ultra thick,fill=earth](C1,A)(-180)
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\tkzDrawSector[rotate,ultra thick,fill=earth](C2,B)(180)
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%
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\tkzCircumCenter(A,A1,B)
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\tkzGetPoint{O}
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\tkzDrawCircle(O,A1)
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%
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\tkzDefLine[perpendicular=through A1,K=-1](A1,C1)
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\tkzGetPoint{x}
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\tkzInterLL(A1,x)(C2,B)
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\tkzGetPoint{H}
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\tkzInterLC(A1,H)(O,A1)
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\tkzGetPoints{A2}{r}
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\tkzDrawSegments(A1,A2)
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\tkzMarkRightAngle(C1,A1,A2)
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\tkzDrawPoints(C1,C2)
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\tkzLabelPoints[font=\fontsize{18pt}{19pt}](H,B)
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\tkzLabelPoints[above,font=\fontsize{18pt}{19pt}](A1)
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\tkzLabelPoints[below,font=\fontsize{18pt}{19pt}](B1,A2)
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%
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\tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C1,A1){\emph{a}}
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\tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C1,A){\emph{a}}
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\tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C2,B){\emph{b}}
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\tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C2,H){\emph{a}}
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\tkzLabelSegment[right,font=\fontsize{18pt}{19pt}\selectfont](A1,H){\emph{a + b}}
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\tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](H,B1){\emph{b - a}}
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\tkzLabelSegment[left,font=\fontsize{18pt}{19pt}\selectfont](H,A2){\emph{x}}
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\end{scope}
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%
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\begin{scope}[shift={(0,-17)}]
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\draw [fill=space, thick] (3.5,0) rectangle (23,-6);
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\draw [fill=dida, thick] (1.8,0.5) rectangle (11.2,-0.5);
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\node [right, align=left, color=black, font=\fontsize{23pt}{24pt}\selectfont] at (2,0) {Teorema delle corde};
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\node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-2) {$A_1H : HB = B_1H : HA2$};
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\node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-4) {$A_1H = a+b = HB \Rightarrow b-a = B_1H = HA_2 = x$};
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\end{scope}
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%
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\begin{scope}[shift={(0,-26)}]
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\tkzDefPoint(15,0){C1}
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\tkzDefShiftPoint[C1](\a,0){A}
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\tkzDefShiftPoint[C1](-\a,0){A1}
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\tkzDefShiftPoint[C1](0,-\a-\b){C2}
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\tkzDefShiftPoint[C2](\b,0){B}
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\tkzDefShiftPoint[C2](-\b,0){B1}
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%
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\tkzDrawSector[rotate,ultra thick,fill=earth](C1,A)(-180)
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\tkzDrawSector[rotate,ultra thick,fill=earth](C2,B)(180)
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%
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\tkzCircumCenter(A,A1,B)
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\tkzGetPoint{O}
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\tkzDrawCircle(O,A1)
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%
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\tkzDefLine[perpendicular=through A1,K=-1](A1,C1)
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\tkzGetPoint{x}
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\tkzInterLL(A1,x)(C2,B)
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\tkzGetPoint{H}
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\tkzInterLC(A1,H)(O,A1)
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\tkzGetPoints{A2}{r}
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\tkzDrawSegments(A1,A2 A2,A)
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\tkzMarkRightAngle(C1,A1,A2)
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\tkzLabelPoints[above,font=\fontsize{18pt}{19pt}](A1,A)
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\tkzLabelPoints[below,font=\fontsize{18pt}{19pt}](A2)
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%
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\tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](A1,A){2\emph{a}}
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\tkzLabelSegment[right,font=\fontsize{18pt}{19pt}\selectfont](A1,A2){2\emph{b}}
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\tkzLabelSegment[right,font=\fontsize{18pt}{19pt}\selectfont](A2,A){2\emph{r}}
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\tkzDrawPoint(O)
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\end{scope}
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%
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\begin{scope}[shift={(0,-47)}]
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\draw [fill=space, thick] (3.5,0) rectangle (23,-10);
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\draw [fill=dida, thick] (1.8,0.6) rectangle (11.2,-0.5);
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\node [right, align=left, color=black, font=\fontsize{23pt}{24pt}\selectfont] at (2,0) {Teorema di Pitagora};
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\node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-2) {$(2a)^2 + (2b)^2 = (2r)^2 \Rightarrow a^2 + b^2 = r^2$};
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\node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-4) {$A_a = \frac{1}{2} \pi a^2, \qquad A_b = \frac{1}{2} \pi b^2$};
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\node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-6) {$A_c = \frac{1}{2} \pi r^2$};
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\node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-8) {$A_a + A_b = \frac{1}{2} \pi (a^2 + b^2) = \frac{1}{2} \pi r^2 = \frac{1}{2} A_c, \, \forall a, b \in \mathds{R}$};
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\end{scope}
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%
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\begin{scope}[shift={(0,-59)}]
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\node at (27,0) () {\includegraphics[width=3.7cm]{licenza}};
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\node at (18,-0.1) {\textcolor{black}{\fontsize{14}{15}\selectfont Testo e illustrazioni: @ulaulaman - Gianluigi Filippelli}};
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\end{scope}
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\end{tikzpicture}
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%
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\end{document} |