\documentclass[11pt,a4j,dvipdfmx]{jsarticle}

\usepackage{hyperref,pxjahyper,minijs}
\usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{calc,arrows.meta}

\hypersetup{%}% Feb 19 2025
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm},
	baseurl={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

\textwidth=150mm \textheight=255mm \columnseprule=0pt
\topmargin=-25mm \oddsidemargin=-5mm

\begin{document}
%
%  ===========================以下本文===============================
%
\centerline{\Large\gtfamily\bfseries たけしのコマ大数学科ワークシート}


\bigskip
%\begin{center}
{\Large\gtfamily\bfseries 問62\quad 秋の数学祭り\quad 軌跡問題}

\bigskip
円の直径\textrm{AB}上の\textrm{A}に
点\textrm{P}があります。
この円が中心を軸として右回りに等速で
回転し始めると同時に点\textrm{P}も
\textrm{AB}上を
等速で進み、円が$1$回転する間に\textrm{B}に到着した時、
点\textrm{P}はどのような軌跡を描くでしょうか？


\centerline{%
\begin{tikzpicture}[scale=1.5,thick, >=stealth,
	baseline=(current bounding box.north)]
\draw[semithick](135:1.5)--(-45:1.5)
	(90:1.5)--(-90:1.5)
	(45:1.5)--(-135:1.5);

\draw(0,0) circle(1.5);
\draw[-{Stealth[length=2ex]}](-1.5,0) node[left]{\textrm{A}}
	--(1.5,0) node[right]{\textrm{B}};
\fill(0,0) circle(1.2pt);
\fill(-1.5,0)
	circle(1.6pt) node[above right]{\textrm{P}};
\draw[-{Stealth[length=1.4ex]},line width=0.2ex](115:1.8)
	arc[start angle=115,end angle=65,radius=1.8];

\foreach \i in {0,45,90,135}{%
	\foreach \x in {-3,...,3}{%
		\draw[rotate around={\i:(0,0)}](3*\x/8,-0.03)--+(0,0.06);
		}
	}
\end{tikzpicture}
}

\vskip6zh


\newcommand{\en}[2]{%
\begin{tikzpicture}[scale=1,semithick, >=stealth,
	baseline=(current bounding box.north)]
\useasboundingbox(-1.5,-1.5,0) grid (1.5,1.5);

\draw(0,0) circle(1.5);
\draw[-{Stealth[length=2ex]}](#1:1.5)--({#1+180}:1.5);
\fill(0,0) circle(1.2pt);
\foreach \x in {-3,...,3}
	\draw[rotate around={#1:(0,0)}](3*\x/8,-0.05)--+(0,0.1);
#2
\end{tikzpicture}
	}

\en{180}{\fill(-1.5,0) circle(2pt) node[above]{P};
	\draw(0,1.8) node{\gtfamily\bfseries スタート};
	\draw(3,0) node{\LARGE ⇒};
	}
\hfill
\en{135}{\draw(3,0) node{\LARGE ⇒};}
\hfill
\en{90}{\fill(0,0.75) circle(2pt) node[left]{P};
	\draw(2.4,0) node{\LARGE ⇒};}


\vskip7ex

\en{45}{\draw(-2.4,0) node{\LARGE ⇒};
	\draw(3,0) node{\LARGE ⇒};
	}
\hfill
\en{0}{\fill(0,0) circle(2pt) node[above]{P};
	\draw(0,1.8) node{\gtfamily\bfseries ちょうど中間};
	\draw(3,0) node{\LARGE ⇒};
	}
\hfill
\en{-45}{\draw(2.4,0) node{\LARGE ⇒};}


\vskip7ex

\en{-90}{\draw(-2.4,0) node{\LARGE ⇒};
	\draw(3,0) node{\LARGE ⇒};
	}
\hfill
\en{-135}{\draw(3,0) node{\LARGE ⇒};}
\hfill
\en{-180}{\fill(1.5,0) circle(2pt) node[above]{P};
	\draw(0,1.8) node{\gtfamily\bfseries ゴール};}



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


{\gtfamily\bfseries （問62 軌跡問題の答え）}


\begin{tikzpicture}[scale=1,thin, >=stealth,
	baseline=(current bounding box.north)]
\draw(0,0) circle(1);
\draw(-1,0)--(1,0);

%■ 媒介変数表示
\draw[very thick,domain=180:-180,smooth,variable=\t]
	plot ({\t*cos(\t)/180},{\t*sin(\t)/180});
\end{tikzpicture}








\end{document}

