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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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	Latex source file: /tmp/Slides/Chord.tex
	No of lines/chars: 109, 2783 chars
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001: \documentclass[tikz,dvipsnames]{standalone}
002: %%% Original latex doc: /usr/local/Slides/2_Palestras/2023/01_PyTikZ/03_TikZ/02_GeoAx/07_Examples/04_Circle/Chord.tikz.tex
003: 
004: 
005: %%!
006: %%! Preamble located by /usr/lib/cgi-bin/tikz2png
007: \input{/usr/local/Slides/2_Palestras/2023/01_PyTikZ/03_TikZ/PreAmble.tikz.tex}
008: %%!
009: 
010: 
011: \newcommand{\Path}{/usr/local/Slides/2_Palestras/2023/01_PyTikZ/03_TikZ/02_GeoAx/07_Examples/04_Circle}
012: \newcommand{\TiKZPath}{/usr/local/tikz}
013: 
014: %%!
015: 
016: 
017: \begin{document}
018: \begin{tikzpicture}%[trig format=rad]
019: %Center, (O), \r, radius of main circle should be predefined.
020: %\alphap and \alphaq as well: Angles for P and Q respective
021: 
022: %Angle for external point, R
023: \pgfmathparse{(\alphap+\alphaq)*0.5}  \let\alpha\pgfmathresult;
024: 
025: %Unit length coordinates of P, Q and E
026: \pgfmathparse{cos(\alphap)} \let\px\pgfmathresult;
027: \pgfmathparse{sin(\alphap)} \let\py\pgfmathresult;
028: 
029: \pgfmathparse{cos(\alphaq)} \let\qx\pgfmathresult;
030: \pgfmathparse{sin(\alphaq)} \let\qy\pgfmathresult;
031: 
032: \pgfmathparse{cos(\alpha)} \let\ex\pgfmathresult;
033: \pgfmathparse{sin(\alpha)} \let\ey\pgfmathresult;
034: 
035: 
036: \coordinate (P) at ($(O)+\r*(\px,\py)$);
037: \coordinate (Q) at ($(O)+\r*(\qx,\qy)$);
038: 
039: \coordinate (NP) at ($(-\py,\px)$);
040: \coordinate (NQ) at ($(-\qy,\qx)$);
041: 
042: \coordinate (P) at ($(O)+\r*(\px,\py)$);
043: 
044: 
045: \pgfmathparse{\r*(\qx-\px)} \let\pqx\pgfmathresult;
046: \pgfmathparse{\r*(\qy-\py)} \let\pqy\pgfmathresult;
047: 
048: %Length of segment PQ: a=|PQ|
049: \pgfmathparse{(\px-\qx)*(\px-\qx)+(\py-\qy)*(\py-\qy)} \let\a\pgfmathresult;
050: \pgfmathparse{\r*sqrt(\a)/2} \let\a\pgfmathresult;
051: 
052: %Distance of segment PQ from origin
053: \pgfmathparse{sqrt(\r*\r-\a*\a)} \let\b\pgfmathresult;
054: 
055: %Distance from midpoint of PQ to focal point: c
056: \pgfmathparse{(0.5*(\r*\r+\a*\a-\b*\b)/\b} \let\c\pgfmathresult;
057: \pgfmathparse{\a*\a/\b} \let\c\pgfmathresult;
058: 
059: %Distance from P or Q Q to focal point: d
060: \pgfmathparse{(\a*\a+\c*\c/(\b*\b)} \let\d\pgfmathresult;
061: \pgfmathparse{sqrt(\d)} \let\d\pgfmathresult;
062: 
063: 
064: \coordinate (S) at ($(O)+\b*(\ex,\ey)$);
065: \coordinate (R) at ($(S)+\c*(\ex,\ey)$);
066: 
067: \filldraw[test,]
068:    (S)  circle(1pt)
069:    node [anchor=north east]{$S$}
070:    ;
071: \filldraw[test,]
072:    (R)  circle(1pt)
073:    node [anchor=south]{$R$}
074:    ;
075: 
076: \coordinate (PQ) at (\pqx,\pqy);
077: 
078: 
079: 
080: 
081: \tkzLabelSegment[test,pos=0.5,below](O,P) { $r$};
082: \tkzLabelSegment[test,pos=0.5,below](O,Q) { $r$};
083: \tkzLabelSegment[test,pos=0.25,below](P,Q) { $a$};
084: \tkzLabelSegment[test,pos=0.75,below](P,Q) { $a$};
085: \tkzLabelSegment[test,pos=0.5,right](O,S) { $b$};
086: \tkzLabelSegment[test,pos=0.5,right](S,R) { $c$};
087: 
088: \tkzLabelSegment[test,pos=0.5,left](P,R) { $d$};
089: \tkzLabelSegment[test,pos=0.5,right](Q,R) { $d$};
090: 
091: \tkzMarkRightAngle[test,](O,Q,R);
092: \tkzMarkRightAngle[test,](O,P,R);
093: 
094: \tkzMarkRightAngle[test,](P,S,R);
095: \tkzMarkRightAngle[test,](Q,S,R);
096: 
097: 
098: %Main circle
099: \draw [name path=c](O) circle(\r);
100: 
101: 
102: \draw [art](P) -- (O) -- (Q);
103: 
104: 
105: \draw  [test,](O) -- (R);
106: 
107: \end{tikzpicture}
108: \end{document}
109: 
###############################
