\documentclass[11pt,b4j,dvipdfmx,landscape,twocolumn,papersize]{jsarticle}
% furikana.sty	http://xymtex.com/fujitas2/texlatex/index.html#tategumi
\usepackage{ascmac,bm,amssymb}
\usepackage[deluxe]{otf}
\usepackage{graphicx,color}
%\usepackage{qrcode}
%\usepackage[pdfpagemode=FullScreen,setpagesize=false]{hyperref}
%\usepackage[pdfstartview={XYZ null null 1.75},setpagesize=false]{hyperref}
\usepackage{hyperref,pxjahyper}
\usepackage{tikz}
\usetikzlibrary{calc}
%\usetikzlibrary{intersections,patterns,angles,backgrounds,positioning}

%\AtBeginDvi{\special{pdf:pagesize width 364mm height 257mm}}
\textwidth=330truemm \textheight=226truemm \columnseprule=0pt
\topmargin=-24truemm \oddsidemargin=-8truemm

\hypersetup{% Oct 1 2023
	pdftitle={数学授業プリント},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/math_ia/math_ia.htm}
	}

\newenvironment{nidan}{\begin{minipage}[t]{.225\textwidth}}{\end{minipage}}
%\def\nidangumi#1#2{\begin{nidan}{#1}\end{nidan}\quad%
%\begin{nidan}{#2}\end{nidan}}
\newcommand{\nidangumi}[2]{\begin{nidan}{#1}\end{nidan}\quad%
\begin{nidan}{#2}\end{nidan}}

% ■■■ 0より大きいときはdvipdfmxで印刷用PDFを作ることを想定（答えはプリント
% 下部に出力される）
%        0 のときはdvipdfmxでデジタル教材用PDFを作ることを想定（答えは問題の
% すぐ横に赤で出力され、後でOneNoteで黒く塗りつぶし）
\def\make_pdf_with_insatsu{1}

\everymath{\displaystyle}
\parindent=0zw \columnsep=3zw
\lineskiplimit=1ex \normallineskiplimit=\lineskiplimit 
\lineskip=\lineskiplimit \normallineskip=\lineskiplimit

\newcounter{toi} \newcounter{subtoi}[toi]
\newcounter{subsubtoi}[subtoi]

\def\toi{\refstepcounter{toi}\par          % 問
  \makebox[2zw][r]{\Large\ajKaku{\value{toi}}\hspace{0.5zw}}%
  \hangindent=2zw}

\def\subtoi{\refstepcounter{subtoi}\par    % 小問
  \makebox[3.4zw][r]{\ajKakko{\value{subtoi}}\hspace{1zw}}%
  \hangindent=3.4zw}

\def\subsubtoi{\refstepcounter{subsubtoi}\par    % 小小問
  \makebox[4.2zw][r]{\ajMaru{\value{subtoi}}\hspace{1zw}}%
  \hangindent=4.2zw}

\ifnum\make_pdf_with_insatsu>0
	\def\kotae#1{\relax}
\else
	\def\kotae#1{\hfill \textcolor{red}{\footnotesize\gtfamily\bfseries\(\boldsymbol{#1} \)}}
\fi

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-0.2em／\hfil\crcr$#1$}}
\pagestyle{empty}

\makeatletter
\def\hooklen#1#2{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother


\begin{document}
%
%  ===========================以下本文===============================
%

\def\namae{%
{\Large\gtfamily\bfseries 数学I \quad 授業プリント \# 52}\hfill
年\hskip8ex 組\hskip8ex 号 \hskip5ex

\hfill 
\underline{氏名\rule[-2ex]{0cm}{6ex}\hskip30ex}}

\namae

\vskip-2ex

{\large\gtfamily\bfseries ■　三角形の面積}

\unitlength=1mm

三角比を使うと『二辺とその間の角度』がわかったときの，三角形の
面積を求めることが出来る。

\begin{center}
\begin{minipage}[t]{0.4\textwidth}
\begin{shadebox}

\begin{large}
\[（三角形の面積）= {\,1\, \over 2}\times （辺の長さ）\times （辺の
長さ）\times \sin （間の角度）\]
\end{large}
%%%%\vspace*{.1ex}

\end{shadebox}
\end{minipage}
\end{center}


\fbox{例題}\quad 右の三角形の面積を求めなさい。
\hskip7zw
\begin{tikzpicture}[rotate=0, scale=0.5, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (C) at (60:4);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw[dashed] (A) to[out=90,in=215] node [inner sep=2pt, fill=white]{\small $4$} (C);
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $5$} (B);
\draw(A) +(32pt,16pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}

\vspace*{-13ex}
\quad
\fbox{解}\qquad
\begin{minipage}[t]{0.15\textwidth}
\vspace*{-5ex}
\begin{eqnarray*}
面積 &=& {\,1\, \over 2}\times 4\times 5\times \sin 60^\circ\\
&=& {\,1\, \over 2}\times 4\times 5\times {\sqrt{3}\over 2}\\
&=& {\,1\, \over {}_{\displaystyle1}\Slash{2}}\times \Slash{4}^{{\Slash{{\displaystyle2}}}^{\displaystyle1}}%
\times 5\times {\sqrt{3}\over \Slash{2}_{\displaystyle1}}\\
&=& 5\sqrt{3}\quad\mbox{\□答}
\end{eqnarray*}
\end{minipage}

\bigskip

\toi 次の三角形の面積を求めなさい。

\nidangumi{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.4, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (7,0);
\coordinate (C) at (30:6);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=60,in=190] node [inner sep=2pt, fill=white]{\small $6$} (C);
\draw[dashed] (A) to[out=-20,in=200] node [inner sep=2pt, fill=white]{\small $7$} (B);
\draw(A) +(48pt,12pt) node{\footnotesize $30^\circ$};
\end{tikzpicture}\kotae{{21\over2}}
}
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.7, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (C) at ($ ({5-2*cos(30)},{2*sin(30)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (B) circle (12pt);
\end{scope}
\draw[dashed] (C) to[out=0,in=100] node [inner sep=2pt, fill=white]{\small $2$} (B);
\draw[dashed] (A) to[out=-20,in=200] node [inner sep=2pt, fill=white]{\small $5$} (B);
\draw(B) +(-32pt,7pt) node{\footnotesize $30^\circ$};
\end{tikzpicture}\kotae{{5\over2}}
}

\vfill


\ifnum\make_pdf_with_insatsu>0
	\rotatebox{180}{{\normalsize\gtfamily\bfseries プリント\#53}\scriptsize
	\quad\( \sin 30^\circ={1\over2},~\sin45^\circ={1\over\sqrt{2}},
	~\sin60^\circ={\sqrt{3}\over2} \)\ 
	{\normalsize\ajKaku{1}}~\ajKakko{1}~\( 9\sqrt{2} \)\ 
	\ajKakko{2}~\( 3\sqrt{3} \)\ 
	\ajKakko{3}~\( 10 \)\ \ajKakko{4}~\( 5\sqrt{3} \)\
	\ajKakko{5}~\( 6 \)\ \ajKakko{6}~\( {3\sqrt{2}\over4} \)\ 
	\ajKakko{7}~\( 5 \)\ \ajKakko{8}~\( 15 \)\ 
	\ajKakko{9}~\( 24 \)
	}
\fi


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage

\nidangumi{\subtoi
\begin{tikzpicture}[scale=0.3, >=stealth,
	baseline=(current bounding box.north)]
% ■■■ この部分はソースを改良した ■■■
\coordinate(A) at (0,0);
\coordinate(B) at (220:10);
\coordinate(C) at (265:8);

%\draw[line cap=round](B)--(C);
\draw(B)--(A)--(C)--cycle;

\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw(A) circle (9ex);
\end{scope}

\draw[dashed](B) to[out=60,in=190]
		node[inner sep=2pt, fill=white]{\small $10$}(A)
	to[out=-70,in=60] node[inner sep=2pt, fill=white]{\small $8$}(C);
\draw(A) node[xshift=-0.8em,yshift=-4ex]{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{20\sqrt{2}}
}
{\subtoi
\begin{tikzpicture}[rotate=-100, scale=0.5, >=stealth, 
	baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at (45:4);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] 
	node [inner sep=2pt, fill=white]{\small $4$} (B);
\draw[dashed] (A) to[out=70,in=200] 
	node [inner sep=2pt, fill=white]{\small $4$} (C);
\draw(A) +(36pt,20pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{4\sqrt{2}}
}%


\vfill


\nidangumi{\subtoi
% ■■■ この部分はソースを改良した ■■■
\begin{tikzpicture}[scale=1.2, >=stealth,
	baseline=(current bounding box.north)]
\coordinate(A) at (0,0);
\coordinate(B) at (110:2);
\coordinate(C) at ($ (170:{sqrt(3)}) $);

\draw(B)--(A)--(C)--cycle;

\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw(A) circle (0.8ex);
\end{scope}

\draw[dashed](B) to[out=-45,in=90] 
		node[inner sep=2pt, fill=white]{\small $2$}(A)
	to[out=210,in=-45] 
		node[inner sep=2pt, fill=white]{\small $\sqrt{3}$}(C);
\draw(A) node[xshift=-1.2em,yshift=1.6ex]{\footnotesize $60^\circ$};
\end{tikzpicture}\kotae{\frac{\,3\,}{2}}
}%
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.6, >=stealth, 
	baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at ($ (60:{sqrt(3)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (12pt);
\end{scope}
\draw[dashed] (A) to[out=-20,in=200] 
	node [inner sep=2pt, fill=white]{\small $4$} (B);
\draw[dashed] (A) to[out=90,in=180] 
	node [inner sep=0pt, fill=white]{\small $\sqrt{3}$} (C);
\draw(A) +(24pt,12pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}\kotae{3}
}%


\vfill


\nidangumi{\subtoi
\begin{tikzpicture}[rotate=-65, scale=0.4, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (9,0);
\coordinate (C) at ($ (30:6) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (36pt);
\end{scope}
\draw[dashed] (A) to[out=-20,in=200] node [inner sep=2pt, fill=white]{\small $9$} (B);
\draw[dashed] (A) to[out=60,in=180] node [inner sep=0pt, fill=white]{\small $6$} (C);
\draw(A) +(64pt,28pt) node{\footnotesize $30^\circ$};
\end{tikzpicture}\kotae{{27\over2}}
}%
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.5, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (7,0);
\coordinate (C) at ($ (45:4) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (18pt);
\end{scope}
\draw[dashed] (A) to[out=-20,in=200] node [inner sep=2pt, fill=white]{\small $7$} (B);
\draw[dashed] (A) to[out=90,in=180] node [inner sep=0pt, fill=white]{\small $4$} (C);
\draw(A) +(40pt,12pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{7\sqrt{2}}
}%


\vfill



\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\setcounter{toi}{0}


\def\namae{%
{\Large\gtfamily\bfseries 数学I \quad 授業プリント \# 53}\hfill
年\hskip8ex 組\hskip8ex 号 \hskip5ex

\hfill 
\underline{氏名\rule[-2ex]{0cm}{6ex}\hskip30ex}}

\namae

\vskip-2ex

{\large\gtfamily\bfseries ■　三角形の面積}

\unitlength=1mm

三角比を使うと『二辺とその間の角度』がわかったときの，三角形の
面積を求めることが出来る。

\begin{center}
\begin{minipage}[t]{0.4\textwidth}
\begin{shadebox}

\begin{large}
\[（三角形の面積）= {\,1\, \over 2}\times （辺の長さ）\times （辺の
長さ）\times \sin （間の角度）\]
\end{large}
%%%%\vspace*{.1ex}

\end{shadebox}
\end{minipage}
\end{center}


\hspace*{15mm}
\begin{tikzpicture}[rotate=0, scale=1.2, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1.732,1);
\coordinate (B) at ($ ({sqrt(3)},1) $);% (1.732,1);
\coordinate (A) at (0,0);
\coordinate (C) at ($ ({sqrt(3)},0) $);% (1.732,0);
\draw (A)--(B)--(C)--cycle;
%\draw (1.532,0)--(1.532,0.2)--(1.732,0.2);
\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\draw[dashed] (A) to[out=-30,in=-150] node [solid, inner sep=2pt, fill=white]{\small $\sqrt{3}$} (C);
\draw[dashed] (A) to[out=60,in=180] node [inner sep=2pt, fill=white]{\small $2$} (B);
\draw[dashed] (C) to[out=45,in=-45] node [inner sep=2pt, fill=white]{\small $1$} (B);
\draw(8pt,0) arc [start angle=0, end angle=30,x radius=8pt, y radius=8pt];
\draw(10pt,0) arc [start angle=0, end angle=30,x radius=10pt, y radius=10pt];
\draw(20pt,5pt) node{\footnotesize $30^\circ$};
\draw(B) +(0,-5pt) arc [start angle=270, end angle=210,x radius=5pt, y radius=5pt];
\draw(B) +(-5pt,-10pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}
%
\hspace*{7zw}
%
\begin{tikzpicture}[rotate=0, scale=1.2, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1,1);
\coordinate (B) at (1,1);
\coordinate (A) at (0,0);
\coordinate (C) at (1,0);
\draw (A)--(B)--(C)--cycle;
%\draw (0.8,0)--(0.8,0.2)--(1,0.2);
\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\draw[dashed] (A) to[out=-45,in=-135] node [inner sep=2pt, fill=white]{\small $1$} (C);
\draw[dashed] (A) to[out=90,in=180] node [solid, inner sep=1pt, fill=white]{\small $\sqrt{2}$} (B);
\draw[dashed] (C) to[out=45,in=-45] node [inner sep=2pt, fill=white]{\small $1$} (B);
\draw(5pt,0) arc [start angle=0, end angle=45,x radius=5pt, y radius=5pt];
\draw(12pt,5pt) node{\footnotesize $45^\circ$};
\draw(B) +(0,-5pt) arc [start angle=270, end angle=225,x radius=5pt, y radius=5pt];
\draw(B) +(-5pt,-13pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}
%
\hspace*{7zw}
%
\begin{tikzpicture}[rotate=0, scale=1.2, baseline=(current bounding box.south)]
%\coordinate [label=above:{\footnotesize B}] (B) at (1,1.732);
\coordinate (B) at ($ (1,{sqrt(3)}) $);% (1,1.732);
\coordinate (A) at (0,0);
\coordinate (C) at (1,0);
\draw (A)--(B)--(C)--cycle;
%\draw (0.8,0)--(0.8,0.2)--(1,0.2);
\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\draw[dashed] (A) to[out=-45,in=-135] node [inner sep=2pt, fill=white]{\small $1$} (C);
\draw[dashed] (A) to[out=90,in=210] node [inner sep=2pt, fill=white]{\small $2$} (B);
\draw[dashed] (C) to[out=45,in=-45] node [inner sep=2pt, fill=white]{\small $\sqrt{3}$} (B);
\draw(5pt,0) arc [start angle=0, end angle=60,x radius=5pt, y radius=5pt];
\draw(12pt,5pt) node{\footnotesize $60^\circ$};
\draw(B) +(0,-8pt) arc [start angle=270, end angle=240,x radius=8pt, y radius=8pt];
\draw(B) +(0,-10pt) arc [start angle=270, end angle=240,x radius=10pt, y radius=10pt];
\draw(B) +(-5pt,-20pt) node{\footnotesize $30^\circ$};
\end{tikzpicture}

\bigskip

\quad\( \sin 30^\circ =\) 
	\raisebox{0mm}{\fbox{\rule[-5mm]{0mm}{12mm}\hskip 15 mm}}\hfill
\( \sin 45^\circ =\) 
	\raisebox{0mm}{\fbox{\rule[-5mm]{0mm}{12mm}\hskip 15 mm}}\hfill
\( \sin 60^\circ =\) 
	\raisebox{0mm}{\fbox{\rule[-5mm]{0mm}{12mm}\hskip 15 mm}}\hfill\mbox{}

\kotae{\sin 30^\circ={1\over2},~\sin45^\circ={1\over\sqrt{2}},
	~\sin60^\circ={\sqrt{3}\over2}}

\bigskip

\toi 次の三角形の面積を求めなさい。


\nidangumi{\subtoi
\begin{tikzpicture}[rotate=30, scale=0.36, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at (45:9);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=-60,in=240] node [inner sep=0pt, fill=white]{\small $4$} (B);
\draw[dashed] (A) to[out=70,in=200] node [inner sep=2pt, fill=white]{\small $9$} (C);
\draw(A) +(48pt,12pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{9\sqrt{2}}
}%
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.6, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at ($ ({4-3*cos(60)},{3*sin(60)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (B) circle (12pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=2pt, fill=white]{\small $4$} (B);
\draw[dashed] (B) to[out=90,in=-30] node [inner sep=2pt, fill=white]{\small $3$} (C);
\draw(B) +(-24pt,12pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}\kotae{3\sqrt{3}}
}%


\vfill


\ifnum\make_pdf_with_insatsu>0
	\rotatebox{180}{{\normalsize\gtfamily\bfseries プリント\#52}\scriptsize
	{\normalsize\ajKaku{1}} \ajKakko{1}~\( {21\over2} \)\ 
	\ajKakko{2}~\( {5\over2} \)\ 
	\ajKakko{3}~\( 20\sqrt{2} \)\ \ajKakko{4}~\( 4\sqrt{2} \)\ 
	\ajKakko{5}~\( {3\over2} \)\ \ajKakko{6}~\( 3 \)\ 
	\ajKakko{7}~\( {27\over2} \)\ \ajKakko{8}~\( 7\sqrt{2} \)
	}
\fi


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage


\nidangumi{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.36, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (C) at (30:8);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=-45,in=225] node [inner sep=0pt, fill=white]{\small $5$} (B);
\draw[dashed] (A) to[out=60,in=180] node [inner sep=2pt, fill=white]{\small $8$} (C);
\draw(A) +(64pt,12pt) node{\footnotesize $30^\circ$};
\end{tikzpicture}\kotae{10}
}%
{\subtoi
\begin{tikzpicture}[rotate=-131, scale=0.36, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (C) at (60:4);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=0pt, fill=white]{\small $5$} (B);
\draw[dashed] (A) to[out=80,in=190] node [inner sep=2pt, fill=white]{\small $4$} (C);
\draw(A) +(36pt,20pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}\kotae{5\sqrt{3}}
}%


\vfill


\nidangumi{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.4, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (6,0);
\coordinate (C) at (30:4);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=0pt, fill=white]{\small $6$} (B);
\draw[dashed] (A) to[out=60,in=180] node [inner sep=1pt, fill=white]{\small $4$} (C);
\draw(A) +(48pt,12pt) node{\footnotesize $30^\circ$};
\end{tikzpicture}\kotae{6}
}%
{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.9, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (3,0);
\coordinate (C) at (45:1);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (10pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=0pt, fill=white]{\small $3$} (B);
\draw[dashed] (A) to[out=90,in=180] node [inner sep=1pt, fill=white]{\small $1$} (C);
\draw(A) +(20pt,6pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{{3\sqrt{2}\over4}}
}%



\vfill


\nidangumi{\subtoi
\begin{tikzpicture}[rotate=-147, scale=0.5, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at (5,0);
\coordinate (C) at ($ (45:{2*sqrt(2)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (16pt);
\end{scope}
\draw[dashed] (A) to[out=-30,in=210] node [inner sep=0pt, fill=white]{\small $5$} (B);
\draw[dashed] (A) to[out=90,in=170] node [inner sep=0pt, fill=white]{\small $2\sqrt{2}$} (C);
\draw(A) +(36pt,16pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{5}
}%
{\subtoi
\begin{tikzpicture}[rotate=80, scale=0.4, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (0,0);
\coordinate (B) at ($ ({2*sqrt(10)},0) $);
\coordinate (C) at ($ (60:{sqrt(30)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (A) to[out=-45,in=225] node [inner sep=0pt, fill=white]{\small $2\sqrt{10}$} (B);
\draw[dashed] (A) to[out=90,in=200] node [inner sep=1pt, fill=white]{\small $\sqrt{30}$} (C);
\draw(A) +(32pt,16pt) node{\footnotesize $60^\circ$};
\end{tikzpicture}\kotae{15}
}%


\vfill


\nidangumi{\subtoi
\begin{tikzpicture}[rotate=0, scale=0.28, >=stealth, baseline=(current bounding box.north)]
%\coordinate [label=left:{\footnotesize A}] (A) at (0,0);
\coordinate (A) at (8,0);
\coordinate (B) at (0,0);
\coordinate (C) at ($ ({8-6*sqrt(2)*cos(45)},{6*sqrt(2)*sin(45)}) $);
\draw (A)--(B)--(C)--cycle;
%\draw (C) ++(-0.2,0)-- ++(0,0.2) -- ++(0.2,0);
\begin{scope}
\clip (A)--(B)--(C)--cycle;
\draw (A) circle (24pt);
\end{scope}
\draw[dashed] (B) to[out=-30,in=210] node [inner sep=0pt, fill=white]{\small $8$} (A);
\draw[dashed] (C) to[out=-10,in=100] node [inner sep=1pt, fill=white]{\small $6\sqrt{2}$} (A);
\draw(A) +(-48pt,18pt) node{\footnotesize $45^\circ$};
\end{tikzpicture}\kotae{24}
}{}


\vfill




\end{document}
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