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\@author% <------ Authors
\end{tabular}\par}% <------
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%opening
\newcommand{\snovdn}{Obodni in središčni kot }
\newcommand{\predmdn}{mat}
\newcommand{\stevilkadn}{14}
\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}
\newcommand{\@xslalph}[1]{%
\ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
\or t\or u\or v\or z\or \v{z}
\else\@ctrerr\fi%
}
\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
\makeatother
\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
\newcommand*\textfrac[2]{
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\renewcommand\abstractname{Povzetek}
\date{26. oktober 2020}
\renewcommand\contentsname{Kazalo vsebine}
\renewcommand\figurename{Slika}
\renewcommand\abstractname{Povzetek}
\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 23. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učnega lista profesorja Domajnka in vaj. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno.
\end{abstract}
\tableofcontents
\section{Vaje \textit{Matematika 2}: stran 29 --- Trikotnik}
\begin{enumerate}[label=\textbf{\arabic*.}]
\setcounter{enumi}{165}
\item[\textbf{166.*}] Načrtaj trikotnik $ABC$ z dano razliko dolžin stranic. Napiši postopek načrtovanja.
\begin{enumerate}[label=\textbf{\xslalph*)}] % c b
\setcounter{enumii}{1}
\item $a-c=\cm{2}, \gamma=\ang{30}, v_a=\cm{4}$
\input{166b.tex}
\lstinputlisting[language=TeX]{166b.tex}
\item $b-c=\cm{1}, \gamma=\ang{60}, a=\cm{3}$
\input{166c.tex}
\lstinputlisting[language=TeX]{166c.tex}
\end{enumerate}
\end{enumerate}
\section{Učni list \textit{\snovdn}}
\begin{enumerate}[label=\textbf{\arabic*.}]
\item Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % b
\begin{enumerate}[label=\textbf{\alph*)}]
\setcounter{enumii}{1}
\item $b=6, \alpha=\ang{30}, \beta=\ang{15}$
\begin{figure}[!h]
\makebox[\textwidth][c]{
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(6,0){K0}
\tkzInterCC(A,K0)(K0,C) \tkzGetPoints{K60}{K60X}
\tkzDefMidPoint(K60,K0) \tkzGetPoint{K30}
\tkzInterLC(K30,A)(A,K0) \tkzGetPoints{C}{CX}
\tkzInterLC(C,A)(C,A) \tkzGetPoints{AX}{AAGAIN}
\tkzDrawLine(A,AX) \tkzLabelLine[above left](A,C){$b$}
\tkzCompass(C,AX) \tkzCompass(A,K0) \tkzCompass(A,C)
\tkzInterCC(C,AX)(AX,C) \tkzGetPoints{G60X}{G60}
\tkzCompass(C,G60) \tkzCompass(AX,G60)
\tkzDefMidPoint(AX,G60) \tkzGetPoint{G30}
\tkzCompass(AX,G30) \tkzCompass(G60,G30)
\tkzInterLC(C,G30)(C,AX) \tkzGetPoints{XX}{X}
\tkzCompass(C,X) \tkzDrawLine(C,G30)
\tkzDefMidPoint(X,G60) \tkzGetPoint{G45}
\tkzCompass(X,G45) \tkzCompass(G60,G45)
\tkzInterLL(C,G45)(A,K0) \tkzGetPoint{B}
\tkzDrawLine(A,B) \tkzLabelLine[below](A,B){$c$}
\tkzDrawLine(C,B) \tkzLabelLine[above right](C,B){$a$}
\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
\end{tikzpicture}
}
\end{figure}
\end{enumerate}
\item Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a
\begin{enumerate}[label=\textbf{\alph*)}]
\item $a=6, b=5, c=10$
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(10,0){B}
\tkzDefPoint(5,0){bH} \tkzDefPoint(4,0){aH}
\tkzDrawLine(A,B) \tkzLabelLine[below](A,B){$c$} \tkzCompass(A,B)
\tkzInterCC(A,bH)(B,aH) \tkzGetPoints{C}{CX}
\tkzCompass(A,C) \tkzCompass(B,C)
\tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$}
\tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$}
\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
\tkzDrawPoints(A) \tkzLabelPoints(A,B,C)
\end{tikzpicture}
\end{center}
\end{enumerate}
\if\false1
\item[\textbf{*3.}] Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % ~c~=>b
\setcounter{enumi}{3}
\begin{enumerate}[label=\textbf{\alph*)}]
\setcounter{enumii}{1}
\item $c=8, a-b=2, \beta=\ang{60}$
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(8,0){B}
\tkzCompass(A,B) \tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$}
\tkzInterCC(A,B)(B,A) \tkzGetPoints{aH}{aHX} \tkzDrawLine(B,aH)
\tkzCompass(A,aH) \tkzCompass(B,aH)
\tkzDrawPoints(A) \tkzLabelPoints(A,B)
\end{tikzpicture}
\end{center}
\end{enumerate}
\fi
\item Načrtaj enakokraki trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % 2
\begin{enumerate}[label=\textbf{\alph*)}]
\setcounter{enumii}{1}
\item $c=7, \gamma=\ang{30}$
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(7,0){B}
\tkzDefMidPoint(A,B)\tkzGetPoint{M}\tkzCompass(A,M) \tkzCompass(B,M)
\tkzInterLC(A,B)(B,M) \tkzGetPoints{AAGAIN}{AX} \tkzCompass(B,AX)
\tkzInterLC(A,B)(A,M) \tkzGetPoints{BX}{BAGAIN} \tkzCompass(A,BX)
\tkzCompass(A,B) \tkzDrawLine[add=0 and 0](BX,AX) \tkzLabelLine[above](A,B){$c$}
\tkzInterCC(A,BX)(BX,A) \tkzGetPoints{A60X}{A60}
\tkzCompass(A,A60) \tkzCompass(BX,A60)
\tkzInterCC(B,AX)(AX,B) \tkzGetPoints{B60}{B60X}
\tkzCompass(B,B60) \tkzCompass(AX,B60)
\tkzInterCC(A60,A)(A,A60) \tkzGetPoints{A120}{BXAGAIN}
\tkzCompass(A,A120) \tkzCompass(A60,A120)
\tkzInterCC(B60,B)(B,B60) \tkzGetPoints{AXAGAIN}{B120}
\tkzCompass(B,B120) \tkzCompass(B60,B120)
\tkzDefMidPoint(A60,A120) \tkzGetPoint{A90}
\tkzInterLC(A,A90)(A,A120) \tkzGetPoints{A90CX}{A90C}
\tkzCompass(A,A90C) \tkzDrawLine(A,A90C)
\tkzDefMidPoint(B60,B120) \tkzGetPoint{B90}
\tkzInterLC(B,B90)(B,B120) \tkzGetPoints{B90CX}{B90C}
\tkzCompass(B,B90C) \tkzDrawLine(B,B90C)
\tkzDefMidPoint(A120,A90C) \tkzGetPoint{A75}
\tkzCompass(A120,A75) \tkzCompass(A90C,A75)
\tkzDefMidPoint(B120,B90C) \tkzGetPoint{B75}
\tkzCompass(B120,B75) \tkzCompass(B90C,B75)
\tkzInterLL(A,A75)(B,B75) \tkzGetPoint{C}
\tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$}
\tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$}
\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
\tkzDrawPoints(A) \tkzLabelPoints(A,B,C)
\end{tikzpicture}
\end{center}
\end{enumerate}
\if\false1
\item Načrtaj pravokotni trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a
\begin{enumerate}[label=\textbf{\alph*}]
\item[\textbf{*b)}] $a+c=12, \alpha=\ang{60}$
\end{enumerate}
\fi
\item[\textbf{*6.}] Načrtaj enakostranični trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a
\begin{enumerate}[label=\textbf{\alph*)}]
\item $a+v=10$
\begin{figure}[H]
\begin{tikzpicture}
\tkzDefPoint(0,0){M} \tkzDefPoint(0,10){N}
\tkzInterCC(M,N)(N,M) \tkzGetPoints{K60}{K60X}
\tkzCompass(M,K60) \tkzCompass(N,K60) \tkzCompass(M,N)
\tkzDefMidPoint(M,K60) \tkzGetPoint{K30}
\tkzDrawLine(N,K30) \tkzInterLC(N,K30)(N,M) \tkzGetPoints{A4L}{K30C}
\tkzCompass(N,K30C) \tkzDefMidPoint(K30C,M) \tkzGetPoint{K15}
\tkzDefMidPoint(M,N) \tkzGetPoint{MN}
\tkzCompass(M,MN) \tkzCompass(N,MN)
\tkzInterLC(M,N)(M,MN) \tkzGetPoints{NX}{NAGAIN} \tkzCompass(M,NX)
\tkzDrawLine(NX,N) \tkzLabelLine[above left](M,N){$v+a$}
\tkzInterCC(MN,NX)(NX,MN) \tkzGetPoints{P}{R}
\tkzInterLL(P,R)(N,K15)\tkzGetPoint{A}\tkzDrawLine[add=0 and 0](P,R)
\tkzDrawLine(N,K15) \tkzInterCC(A,N)(N,A) \tkzGetPoints{AL}{L60}
\tkzCompass(A,L60) \tkzCompass(N,L60)
\tkzDefMidPoint(L60,N) \tkzGetPoint{L30} \tkzInterLC(A,L30)(A,N)
\tkzGetPoints{L30CX}{L30C}\tkzCompass(A,L30C)\tkzDrawLine(A,L30)
\tkzDefMidPoint(L30C,N) \tkzGetPoint{L15} \tkzDrawLine(A,L15)
\tkzCompass(L30C,L15) \tkzCompass(N,L15)
\tkzCompass(K60,K30) \tkzCompass(A,K30)
\tkzCompass(N,L30) \tkzCompass(L60,L30)
\tkzInterLL(M,N)(A,L15) \tkzGetPoint{C}
\tkzInterLC(A,M)(M,A) \tkzGetPoints{AAGAIN}{B} \tkzCompass(M,B)
\tkzDrawLine(C,B) \tkzLabelLine[above right](C,B){$a$}
\tkzLabelLine[above left](C,A){$b$}
\tkzLabelLine[above left](A,B){$c$}
\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
\tkzDrawPoints(M) \tkzLabelPoints(A,C,B) \tkzMarkRightAngles(P,M,N)
\end{tikzpicture}
\end{figure}
\end{enumerate}
\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 \SI{}{\second}.
\fi
% \item $$$$
\end{document}
