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108 lines
3.5 KiB
TeX
108 lines
3.5 KiB
TeX
\documentclass{article}
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\usepackage{xcolor}
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\definecolor{cWinkelhalbierende}{HTML}{00940A}
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\definecolor{cSeitenhalbierende}{HTML}{FF0000}
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\definecolor{cAchse}{HTML} {94008A}
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\definecolor{cMittelsenkrechten}{HTML}{181FED}
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\usepackage[pdftex,active,tightpage]{preview}
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\setlength\PreviewBorder{2mm}
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\usepackage{tikz}
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\usetikzlibrary{shapes, calc}
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\begin{document}
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\begin{preview}
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\begin{tikzpicture}
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\coordinate[label=left:$A$] (A) at (0,0);
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\coordinate[label=right:$B$] (B) at (3.2,0);
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\coordinate[label=left:$C$] (C) at (1.6,4);
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% Draw the background of the triangle
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\node[isosceles triangle, isosceles triangle apex angle=44,draw,
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inner sep=0pt,anchor=lower side,rotate=90,draw=black,
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line width=1.5pt, minimum height=4cm, fill=gray!2]
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(triangle) at (1.6,-0.05) {};
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% Rechte Winkel
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\begin{scope}[shift={($(A)!0.5!(C)$)}, rotate=-22]
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\draw[fill=gray!30] (0,0) -- (-180:0.25cm) arc (180:90:0.25cm);
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\draw (140:0.15cm) node {$\cdot$};
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\end{scope}
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\begin{scope}[shift={($(B)!0.5!(C)$)}, rotate=-70]
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\draw[fill=gray!30] (0,0) -- (-180:0.25cm) arc (180:90:0.25cm);
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\draw (140:0.15cm) node {$\cdot$};
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\end{scope}
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\begin{scope}[shift={($(A)!0.5!(B)$)}]
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\draw[fill=gray!30,draw opacity=0] (0,0) -- (-180:0.25cm) arc (180:90:0.25cm);
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\draw (-180:0.25cm) arc (180:90:0.25cm);
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\draw (140:0.15cm) node {$\cdot$};
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\end{scope}
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% Mittelsenkrechten
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% y = m * x + t
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% Für die Mittelsenkrechte m_AB gilt ($(A)!0.5!(B)$) ist auf m_AB
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% m = - (delta x) / (delta y) = - (A.x - B.x) / (A.y - B.y)
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% t = y - m*x
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% AB
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\draw[color=cAchse, thick] (1.6cm,-0.3) -- node {} (1.6cm, 4.2cm);
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% AC
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% (0.8, 2) \in Mittelsenkrechte auf b
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% m = - (-1.6)/(-4) = - 0.4
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% t = 2 + 0.4 * 0.8 = 2.32
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% y = -0.4 * x + 2.32
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% (0, 2.32) und (3, 1.12)
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\draw[color=cMittelsenkrechten] (0,2.32) -- node {} (3, 1.12);
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% Umkreismittelpunkt
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% x = 1.6
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% y = -0.4*1.6 + 2.32 = 1.68
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\node [circle,inner sep=1pt,fill=cMittelsenkrechten] at (1.6,1.68) {};
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% ((3.2+1.6)/2, (0+4)/2) ) = (2.4, 2) \in Mittelsenkrechte auf a
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% 2 = m * 2.4 + t
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% m_BC = delta y / delta x = (0-4)/(3.2-1.6) = -2.5 = -5/2
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% m = 2/5
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% t = y - m*x = 2 - 2.4 * 2/5 = 1.04
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% => y = 2/5 * x + 1.04
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% (0, 1.04) und (3, 2.24)
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\draw[color=cMittelsenkrechten] (0, 1.04) -- node {} (3, 2.24);
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% Seitenhalbierende
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\draw[color=cSeitenhalbierende,dashed] (A) -- node {} ($(B)!0.5!(C)$);
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\draw[color=cSeitenhalbierende,dashed] (B) -- node {} ($(A)!0.5!(C)$);
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%\draw[color=red, dashed] (C) -- node {} ($(A)!0.5!(B)$);
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% Schwerpunkt
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% x = 1.6
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\node [circle,inner sep=1pt,fill=cSeitenhalbierende] at (1.6,1.34) {};
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% Winkelhalbierende
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% apex angle = 44° => alpha = 68° => 34°
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\draw[color=cWinkelhalbierende, densely dashed] (A) -- node {} (34:4);
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\begin{scope}[shift={($(B)$)}]
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\draw (146:4) node (BEnd) {};
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\end{scope}
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\draw[color=cWinkelhalbierende, densely dashed] (B) -- node {} (BEnd);
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%\draw[color=red, dashed] (C) -- node {} ($(A)!0.5!(B)$);
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% Inkreismittelpunkt
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% x = 1.6
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% tan(68/2) = y/x => y = tan(34)*x = 1.48
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\node [circle,inner sep=1pt,fill=cWinkelhalbierende] at (1.6,1.08) {};
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% Draw the triangle
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\node[isosceles triangle, isosceles triangle apex angle=44,draw,
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inner sep=0pt,anchor=lower side,rotate=90,draw=black,
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line width=1.5pt, minimum height=4cm]
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(triangle) at (1.6,-0.05) {};
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\end{tikzpicture}
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\end{preview}
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\end{document}
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