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%opening
\newcommand{\snovdn}{Trikotnik }
\newcommand{\predmdn}{mat}
\newcommand{\stevilkadn}{11}
\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
\makeatletter
\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
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\renewcommand\abstractname{Povzetek}
\date{19. oktober 2020}
\renewcommand\contentsname{Kazalo vsebine}
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\newcommand{\iic}{I\textsuperscript{2}C }
% \patchcmd{\thebibliography}{\section*{\refname}}{}{}{}
\title{%
\snovdn --- \stevilkadn. domača naloga \\
\large Matematika, Gimnazija Bežigrad}
\author{\begin{tabular}{rl}
\textbf{Profesor:} & prof. Vilko Domajnko \\
\textbf{Avtor:} & Anton Luka Šijanec, 2. a
% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
\end{tabular}}
% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
\begin{document}
\maketitle
\begin{abstract}
Ta dokument obsega naloge, naročene dijakom 19. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učbenika. Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno.
\end{abstract}
\tableofcontents
\section{Učbenik \textit{Matematika 2}: Trikotnik --- stran 33}
\begin{enumerate}[label=\textbf{\arabic*.}]
\setcounter{enumi}{6}
\item Načrtaj trikotnik s podatki: $c=\cm{4}, t_a=\cm{5,5}, \beta=\ang{120}$.
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(4,0){B} \tkzDefPoint(5.5,0){AH}
\tkzInterLC(A,B)(B,A) \tkzGetPoints{AAGAIN}{AX} \tkzCompass(A,B)
\tkzDrawLine(A,AX) \tkzLabelLine[above, pos = 0.25](A,AX){$c$} \tkzCompass(B,AX) \tkzInterCC(B,AX)(AX,B) \tkzGetPoints{CH}{USELESS}
\tkzCompass(B,CH) \tkzCompass(AX,CH)
\tkzDrawLine(B,CH) \tkzLabelLine[above left](B,CH){$a$}
\tkzInterLC(B,CH)(A,AH) \tkzGetPoints{HA}{USELESS}
\tkzCompass(A,HA) \tkzInterLC(B,CH)(HA,B) \tkzGetPoints{BAGAIN}{C}
\tkzCompass(HA,C) \tkzDrawLine(A,C) \tkzLabelLine[below](A,C){$b$}
\tkzDrawPoints(A) \tkzLabelPoints(A,B,C)
\end{tikzpicture}
\end{center}
\newpage
\item Načrtaj trikotnike.
\begin{multicols}{4}
\begin{enumerate}[label=\color{black}\textbf{\xslalph*)}]
\item \color{codered} $$b=\cm{6}$$ $$v_b=\cm{4}$$ $$t_b=\cm{5}$$ % <&=&
\item \color{black} $$a=\cm{5}$$ $$v_a=\cm{3,5}$$ $$\gamma=\ang{75}$$
\item $$c=\cm{6}$$ $$a=\cm{4}$$ $$t_a=\cm{5,5}$$
\item $$b=\cm{5,5}$$ $$t_c=\cm{5}$$ $$\alpha=\ang{60}$$
\end{enumerate}
\end{multicols}
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(69:6){C}
\tkzDefPoint(69:4){VH} \tkzDefPoint(69:-2){TH}
\tkzCompass(A,C) \tkzDrawLine(TH,C) \tkzLabelLine[below right](A,C){$b$}
\tkzDefMidPoint(A,C) \tkzGetPoint{ACM}
\tkzCompass(A,ACM) \tkzCompass(C,ACM)
\tkzDefMidPoint(A,ACM) \tkzGetPoint{AACMM}
\tkzInterLC(A,C)(A,AACMM) \tkzGetPoints{PH1}{PH2}
\tkzCompass(A,PH1) \tkzCompass(A,PH2)
\tkzInterCC(PH1,PH2)(PH2,PH1) \tkzGetPoints{USELESS}{V1}
\tkzCompass(PH1,V1)\tkzCompass(PH2,V1)
\tkzInterLC(A,V1)(A,VH) \tkzGetPoints{USELESS}{V}
\tkzCompass(A,V) \tkzInterLC(A,V)(V,V1) \tkzGetPoints{USELESS}{V1X}
\tkzDrawLine(A,V1X) \tkzCompass(V,V1X) \tkzInterCC(V1,V1X)(V1X,V1)
\tkzGetPoints{VP}{VPX} \tkzCompass(V1,VP) \tkzCompass(V1X,VP)
\tkzDrawLine(VPX,VP) \tkzInterLC(VP,VPX)(ACM,TH) \tkzGetPoints{USELE}{B}
\tkzCompass(ACM,B) \tkzDrawLine(B,C) \tkzLabelLine[below left](B,C){$a$}
\tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$}
\tkzMarkRightAngles(PH1,A,V1 A,V,VP)
\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
\end{tikzpicture}
\end{center}
\item Načrtaj enakokraki trikotnik, katerega višina na osnovnico je dolga $\cm{3}$, kot ob osnovinci pa je velik $\ang{30}$.
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B}
\tkzDrawLine(A,B) \tkzLabelLine[above,pos=.4](A,B){$c$} \tkzCompass(A,B)
\tkzInterCC(A,B)(B,A) \tkzGetPoints{CL}{USELESS}
\tkzCompass(A,B) \tkzCompass(A,CL)
\tkzDefMidPoint(B,CL) \tkzGetPoint{K}\tkzCompass(B,K)\tkzCompass(CL,K)
\tkzDrawLine(A,K)
\tkzDefMidPoint(A,B) \tkzGetPoint{ABM} \tkzInterCC(A,B)(B,A)
\tkzGetPoints{ABP}{ABPX} \tkzCompass(A,ABP) \tkzCompass(B,ABP)
\tkzDrawLine(ABM,ABP) \tkzInterLL(ABPX,ABP)(A,K) \tkzGetPoint{C}
\tkzLabelLine[above left](A,C){$b$}
\tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$}
\tkzDrawPoints(A) \tkzLabelPoints(A)
\tkzLabelPoint[below left](B){$B$} \tkzLabelPoint[above left](C){$C$}
\end{tikzpicture}
\end{center}
\item Načrtaj pravokotni trikotnik s pravim kotom v oglišču $C$, katerega stranica $AC$ je dolga $\cm{4}$, simetrala kota pri $A$ pa $\cm{5}$. Nariši trikotniku včrtano krožnico.
Na tem mestu naj povem, da je \textbf{simetrala kota poltrak} in nima dolžine!
Zato trikotnika ne morem načrtati, zakar tudi včrtanje stranice ni možno. )-:
\if\false1
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(69:4){C}
\tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C)
\tkz
\tkzDrawPoints(A) \tkzLabelPoints(A,C)
\end{tikzpicture}
\end{center}
\fi
\newpage
\item Načrtaj trikotnik in trikotniku očrtano krožnico.
\begin{multicols}{4}
\begin{enumerate}[label=\color{black}\textbf{\xslalph*)}]
\item $$a=\cm{5}$$ $$b=\cm{4}$$ $$\alpha=\ang{75}$$
\item \color{codered} $$b=\cm{3}$$ $$v_b=\cm{4}$$ $$\gamma=\ang{120}$$
\item \color{black} $$a=\cm{4}$$ $$b=\cm{5}$$ $$\gamma=\ang{90}$$
\item $$a=b=\cm{4}$$ $$c=6\cm$$
\end{enumerate}
\end{multicols}
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(69:3){C} \tkzDefPoint(69:4){VHX}
\tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C)
\tkzInterLC(A,C)(C,A) \tkzGetPoints{A}{AX}
\tkzCompass(C,AX) \tkzDrawLine(A,AX) \tkzInterCC(AX,C)(C,AX)
\tkzGetPoints{BH}{BHX} \tkzCompass(AX,BH) \tkzCompass(C,BH)
\tkzDefMidPoint(A,C) \tkzGetPoint{ACM} \tkzCompass(A,ACM)
\tkzInterLC(A,C)(A,ACM) \tkzGetPoints{ACMX}{ACM} \tkzCompass(A,ACMX)
\tkzDrawLine(ACMX,AX)\tkzInterCC(ACMX,ACM)(ACM,ACMX) \tkzGetPoints{Y}{X}
\tkzCompass(ACM,X) \tkzCompass(ACMX,X)
\tkzInterLC(A,X)(A,VHX) \tkzGetPoints{USELESS}{VH}
\tkzCompass(A,VH) \tkzInterLC(A,X)(VH,A) \tkzGetPoints{A}{AXX}
\tkzCompass(VH,AXX) \tkzDrawLine(A,AXX)
\tkzInterCC(A,AXX)(AXX,A) \tkzGetPoints{V2}{V2X}
\tkzCompass(A,V2) \tkzCompass(AXX,V2) \tkzDrawLine(VH,V2)
\tkzInterLL(V2,V2X)(C,BH) \tkzGetPoint{B} \tkzDrawLine(C,B)
\tkzLabelLine[above left](C,B){$a$}
\tkzDrawLine(A,B) \tkzLabelLine[above left](A,B){$c$}
\tkzInterCC(C,B)(B,C) \tkzGetPoints{CBS}{CBSX} % krožnica
\tkzCompass(C,CBS) \tkzCompass(B,CBS) \tkzDrawLine(CBS,CBSX)
\tkzCompass(C,CBSX) \tkzCompass(B,CBSX)
\tkzInterCC(A,B)(B,A) \tkzGetPoints{ABS}{ABSX}
\tkzCompass(A,ABS) \tkzCompass(B,ABS) \tkzDrawLine(ABS,ABSX)
\tkzCompass(A,ABSX) \tkzCompass(B,ABSX)
\tkzInterLL(ABS,ABSX)(CBS,CBSX) \tkzGetPoint{S}
\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
\tkzMarkRightAngles(VH,A,C B,VH,A)
\tkzDrawCircle[fill = red!30,opacity=.3](S,A)
\tkzDrawPolygon[fill=blue!30,opacity=.3](A,B,C) % za razvidnost
\end{tikzpicture}
\end{center}
\end{enumerate}
\section{Zaključek}
Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
\hologo{LaTeX}
izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo mojem šolskem Git repozitoriju na
\url{https://github.com/sijanec/sola-gimb-2} v mapi
\href{https://github.com/sijanec/sola-gimb-2/tree/master/\predmdn/domace_naloge/\stevilkadn/}{/\predmdn/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/domace_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://github.com/sijanec/sola-gimb-2/raw/master/\predmdn/domace_naloge/\stevilkadn/dokument.pdf}.
\if\razhroscevanje1
\section{Razhroščevalne informacije}
Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
Grafi imajo natančnost \functionSamples\space točk na graf.
Konec generiranja dokumenta: \input|"date -Ins"
Dokument se je generiral aaasecgeninsaaa sekund.
\fi
% \item $$$$
\end{document}
