円周角の定理の問題で使った TikZ で作った図とソースです。自分用のソース置き場です。
\documentclass[dvipdfmx,border=2mm,multi=pageSplit]{standalone}
\usepackage{tikz}
\usetikzlibrary{angles,quotes}
\begin{document}
\begin{pageSplit}
\scalebox{1}{%
\begin{tikzpicture}[scale=.6]
% 点を定義
\coordinate[label=above:O] (O) at (0,0);
\coordinate (A) at (120:3);
\coordinate (B) at (210:3);
\coordinate (C) at (330:3);
\coordinate (D) at (75:3);
% 円周角
\draw pic ["$\alpha$",very thick,draw=red,fill=red!10!white,angle eccentricity=1.3,angle radius=5mm] {angle=B--A--C};
\draw pic ["$\alpha$",very thick,draw=red,fill=red!10!white,angle eccentricity=1.3,angle radius=5mm] {angle=B--D--C};
\draw pic ["$2\alpha$",very thick,draw=blue,fill=blue!10!white,angle eccentricity=1.4,angle radius=4mm] {angle=B--O--C};
% 図を描画
\draw (O) circle[radius=3];
\draw[fill] (O) circle[radius=3pt];
\draw (B)--(O)--(C);
\draw[very thick,line join=round] (B)--(A)--(C);
\draw[very thick,line join=round] (B)--(D)--(C);
\end{tikzpicture}
}
\end{pageSplit}
\end{document}

\documentclass[dvipdfmx,border=2mm,multi=pageSplit]{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}
\usetikzlibrary{angles,quotes}
\begin{document}
\begin{pageSplit}
\scalebox{1}{%
\begin{tikzpicture}[scale=.6]
% 点を定義
\coordinate (O) at (0,0);
\coordinate (A) at (95:3);
\coordinate (B) at (200:3);
\coordinate (C) at (265:3);
\coordinate (D) at (340:3);
\path[name path=eAC,overlay] (A)--(C);
\path[name path=eBD,overlay] (B)--(D);
\path[name intersections={of=eAC and eBD}];
\coordinate (X) at (intersection-1);
% 角度
\draw pic ["$\alpha$",draw=black,angle eccentricity=1.3,angle radius=7mm] {angle=B--A--C};
\draw pic ["$\beta$",draw=black,angle eccentricity=1.8,angle radius=3mm] {angle=B--X--C};
\draw pic ["$55^{\circ}$",draw=black,angle eccentricity=2.0,angle radius=4mm] {angle=D--B--A};
\draw pic ["$33^{\circ}$",draw=black,angle eccentricity=2.0,angle radius=4mm] {angle=B--D--C};
% 図を描画
\draw[very thick,line join=round] (A)--(B)--(D)--(C)--cycle;
\draw (O) circle[radius=3];
\end{tikzpicture}
}
\end{pageSplit}
\end{document}

\documentclass[dvipdfmx,border=2mm,multi=pageSplit]{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}
\usetikzlibrary{angles,quotes}
\begin{document}
\begin{pageSplit}
\scalebox{1}{%
\begin{tikzpicture}[scale=.6]
% 点を定義
\coordinate[label=left:O] (O) at (0,0);
\coordinate (A) at (135:3);
\coordinate (B) at (270:3);
\coordinate (C) at (350:3);
\coordinate (D) at (45:3);
\coordinate (X) at (90:3);
% 角度
\draw pic ["$\alpha$",draw=black,angle eccentricity=1.3,angle radius=8mm] {angle=X--B--A};
\draw pic ["$\beta$",draw=black,angle eccentricity=1.5,angle radius=4mm] {angle=A--C--B};
\draw pic ["$48^{\circ}$",draw=black,angle eccentricity=1.5,angle radius=5mm] {angle=D--C--A};
% 等分
\draw ([shift={(0,0)}]45:3) arc[radius=3, start angle=45, end angle= 90] node[midway,sloped] {\scriptsize $\|$};
\draw ([shift={(0,0)}]90:3) arc[radius=3, start angle=90, end angle= 135] node[midway,sloped] {\scriptsize $\|$};
% 図を描画
\draw (O) circle[radius=3];
\draw[fill] (O) circle[radius=3pt];
\draw[very thick,line join=round] (B)--(A)--(C)--(D)--(B)--(C);
\draw[very thick] (X)--(B);
\end{tikzpicture}
}
\end{pageSplit}
\end{document}

ますどら 
