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% !TeX encoding = UTF-8
% !TeX spellcheck = sl_SI
% do-vimlatex-onwrite
\documentclass[]{article}
\usepackage[utf8]{inputenc}
\usepackage{etoolbox}
\usepackage[hidelinks]{hyperref}
\usepackage[a4paper, total={7in, 10in}]{geometry}
\usepackage{graphicx}
\usepackage{hologo}
\usepackage{amssymb}
\usepackage{pgfplots}
\usepackage[inline]{enumitem}
\usepackage{amsmath}
\usepackage{siunitx}
\usepackage{multicol}
\usepackage{tabularcalc}
\usepackage{amsmath}
\usepackage{float}
\usepackage{tasks}
\usepackage{filecontents}
\usepackage{textcomp}
\usepackage{tkz-euclide}
\usepackage{dirtytalk}
\usepackage{csquotes}
\usepackage{listings}
% \usepackage{multienum} % weird with labels
\usetikzlibrary{calc} %% not really needed............. idk.
%\usetikzlibrary{external}
% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
%\tikzexternalize
\usepackage{xcolor}
\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
\newcommand{\razhroscevanje}{0}
\definecolor{codegreen}{rgb}{0,0.6,0}
\definecolor{codegray}{rgb}{0.5,0.5,0.5}
\definecolor{codepurple}{rgb}{0.58,0,0.82}
\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
\lstdefinestyle{mystyle}{
backgroundcolor=\color{backcolour},
commentstyle=\color{codegreen},
keywordstyle=\color{magenta},
numberstyle=\tiny\color{codegray},
stringstyle=\color{codepurple},
basicstyle=\ttfamily\footnotesize,
breakatwhitespace=false,
breaklines=true,
captionpos=b,
keepspaces=true,
numbers=left,
numbersep=5pt,
showspaces=false,
showstringspaces=false,
showtabs=false,
tabsize=2
}
\lstset{style=mystyle}
\def\@maketitle{%
\newpage
\null
\vskip 2em%
\begin{center}%
\let \footnote \thanks
{\LARGE \@title \par}%
\vskip 1.5em%
{\large
\lineskip .5em%
\begin{tabular}[t]{c}% <------
\@author% <------ Authors
\end{tabular}\par}% <------
\vskip 1em%
{\large \@date}%
\end{center}%
\par
\vskip 1.5em}
%opening
\newcommand{\snovdn}{Krožnica, tetiva in tangenta }
\newcommand{\predmdn}{mat}
\newcommand{\stevilkadn}{10}
\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]{
\frac{\text{#1}}{\text{#2}}
}
\renewcommand\abstractname{Povzetek}
\date{16. 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}
% \end{abstract}
% \tableofcontents
% \section{Učni list \textit{\snovdn}: osma naloga --- štirje primeri}
\begin{enumerate}[label=\textbf{\xslalph*)}]
\item Naj bosta $A$ in $B$ točki, ki sta oddaljeni \cm{5}. Nariši krožnico s polmerom \cm{7}, ki gre skozi točki $A$ in $B$.
\item Naj bo $A$ točka, ki je od premice $P$ oddaljena \cm{5}. Nariši krožnico s polmerom \cm{4}, ki gre skozi $A$ in se dotika $p$;
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(5,0){B}
\tkzDefPoint(-7,0){AH} \tkzDefPoint(12,0){BH} % namesto radija v intercc
\tkzDrawLine(A,B) \tkzCompass(A,B)
\tkzInterCC(A,AH)(B,BH) \tkzGetPoints{S}{S2}
\tkzCompass(A,S) \tkzCompass(B,S) \tkzDrawCircle(S,A)
\tkzCalcLength[cm](A,S) \tkzGetLength{dAS}
\tkzDrawSegment[dim={\pgfmathprintnumber\dAS cm,6pt,transform shape}](S,A)
\tkzDefPoint(0,4){PH1} \tkzDefPoint(1,4){PH2}
\tkzDrawLine(PH1,PH2) \tkzLabelLine[above](PH1,PH2){$p$}
\tkzMarkRightAngles(A,PH1,PH2) \tkzDrawLine(A,PH1)
\tkzDrawCircle(A,PH1)
\tkzDrawPoints(A) \tkzLabelPoints(A,B)
\end{tikzpicture}
\end{center}
\setcounter{enumi}{4}
\item Naj bosta $p$ in $q$ premici, ki oklepata kot \ang{60}, $A$ njuno presečišče in $B$ točka na premici $p$, ki je od $A$ oddaljena \cm{5}. Nariši krožnico, ki se dotika obeh premic, premice $p$ v točki $B$.
\item \color{magenta} Naj bosta $p$ in $q$ premici, ki oklepata kot \ang{30}, $A$ njuno presečišče in $B$ točka, na premici $p$, ki je od $A$ oddaljena \cm{5}. Nariši krožnico, ki se dotika premice $p$ v točki $B$, njeno središče pa leži na premici $q$. \color{black} Ta krožnica je enaka krožnici iz prejšnje naloge.
\begin{center}
\begin{tikzpicture}
\tkzDefPoint (0,0){A} \tkzDefPoint (5,0){B}
\tkzDefPoint(3.4,0){BH1} \tkzDefPoint(6.6,0){BH2}
\tkzCompass(A,B) \tkzCompass(B,BH1) \tkzCompass(B,BH2)
\tkzDrawLine[add = 0.2 and 0.4](A,B) \tkzLabelLine[above](A,B){$p$}
\tkzInterCC(A,B)(B,A) \tkzGetPoints{Q}{QX}
\tkzCompass(A,Q) \tkzCompass(B,Q)
\tkzDrawLine[add = 0.2 and 0.4](A,Q) \tkzLabelLine[above left](A,Q){$q$}
\tkzInterCC(BH1,BH2)(BH2,BH1) \tkzGetPoints{BP}{BPX}
\tkzCompass(BH1,BP) \tkzCompass(BH2,BP)
\tkzDrawLine(B,BP) \tkzMarkRightAngles(A,B,BP)
\tkzDefMidPoint(A,Q) \tkzGetPoint{AQM} \tkzDefMidPoint(AQM,Q)
\tkzGetPoint{AQMQM} \tkzInterLC(A,Q)(Q,AQMQM) \tkzGetPoints{QH1}{QH2}
\tkzCompass(Q,QH1) \tkzCompass(Q,QH2)
\tkzInterCC(QH1,QH2)(QH2,QH1) \tkzGetPoints{QPX}{QP}
\tkzCompass(QH1,QP)\tkzCompass(QH2,QP)
\tkzDrawLine[add = 0.2 and 0.4](Q,QP) \tkzMarkRightAngles(A,Q,QP)
\tkzInterLL(Q,QP)(B,BP) \tkzGetPoint{S} \tkzDrawCircle(S,Q)
\tkzDrawPoints(A) \tkzLabelPoints(A,B) \tkzMarkRightAngles(A,B,BP)
\tkzDrawLine[color=magenta](S,A)
\tkzLabelLine[color=magenta, above](S,A){$q$}
% \tkzInterLC(A,S)(B,S) \tkzGetPoints{RPH1}{RPH2}
% \tkzCompass[color=magenta](B,RPH1) \tkzCompass[color=magenta](B,RPH2)
% \tkzDefMidPoint(RPH1,RPH2) \tkzGetPoint{RP}
% \tkzCompass[color=magenta](RPH1,RP) \tkzCompass[color=magenta](RPH2,RP)
% \tkzDrawLine[color=magenta](RP,B)
\tkzDrawCircle[color=magenta](S,B)
% \tkzMarkRightAngles[color=magenta](A,RP,B)
\end{tikzpicture}
\end{center}
\end{enumerate}
\section*{Zaključek}
Ta dokument obsega naloge, naročene dijakom 15. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učnega lista profesorja Domajnka. Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno.
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"
\fi
% \item $$$$
\end{document}
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