京都府立医科大学 前期 2000年度 問4

このコンテンツをご覧いただくためにはJavaScriptをONにし、最新のFlash Playerが必要です。

最新のFlash Playerのインストールはこちら

入試情報

大学名 京都府立医科大学
学科・方式 前期
年度 2000年度
問No 問4
学部 医学部
カテゴリ 積分法の応用
状態 解答なし 解説なし ウォッチリスト

コメントをつけるにはログインが必要です。

コメントはまだありません。

% % すうじあむはアップするファイルで完結したTeXソースでないといけない. % このひな形で表示確認をしよう. % \documentclass[b5paper,fleqn,papersize]{jsarticle} %=========================================================== % ■余白の設定 B5 %----------------------------------------------------------- \setlength{\oddsidemargin}{-5.4truemm} % 左マージン \setlength{\topmargin}{-15.4truemm} % 上マージン \setlength{\textwidth}{14.2cm} % B5 サイズ用 \setlength{\headheight}{2zw} \setlength{\headsep}{2zw} \setlength{\textheight}{217mm} %=========================================================== \usepackage[dvipdfm]{graphicx,color} %\usepackage{wallpaper} \usepackage{wrapfig} \usepackage{amsmath,amsthm,amssymb} \usepackage{multicol} \usepackage{longtable} \usepackage{ascmac} \usepackage{fancybox} \usepackage{framed} \usepackage{ifthen} \usepackage{setspace} % setspaceパッケージのインクルード \usepackage{amssymb}% ≒を表示するために必要 % \usepackage{comment}% コメント% mebio.styと競合する \usepackage{booktabs} \usepackage{ascmac} \usepackage{itembbox} % % \usepackage{ custom_suseum}% すうじあむ %========================================================= %============================================================ % ■ 分数の横棒を長く,分数を立てに狭く(emath.styの古い記述) %------------------------------------------------------------ % 分数記号(分数罫を少し長めに) \newcommand{\bunsuu}[2]{\dfrac{\,#1\,}{\,#2\,}}% % さらに罫線の上下を狭く. \newcommand\Dfrac[2]{\bunsuu{\lower.6ex\hbox{$#1$}}{\lower-.3ex\hbox{$#2$}}}% %============================================================ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % enumerate の自動ラベルの変更 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\labelenumi{(\theenumi)} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 増減表の矢印 % http://www.biwako.shiga-u.ac.jp/sensei/kumazawa/tex/arrow.html % % $\cvinc$ increase % $\ccinc$ concavity 凹状の % $\cvdec$ convex 凸形の % $\ccdec$ decrease % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \makeatletter \newcommand{\ccinc}{\ifx\@currsize\small \setlength{\unitlength}{1.1pt} \begin{picture}(10,10)(1,2) \put(1,2){\line(0,1){3}} \put(5,5){\oval(8,8)[lt]} \put(5,9){\vector(1,0){4}} \end{picture}\else \setlength{\unitlength}{1.2pt} \begin{picture}(10,10)(1,2) \put(1,2){\line(0,1){3}} \put(5,5){\oval(8,8)[lt]} \put(5,9){\vector(1,0){4}} \end{picture}\fi} \newcommand{\cvinc}{\ifx\@currsize\small \setlength{\unitlength}{1.1pt} \begin{picture}(10,10)(2,1) \put(2,1){\line(1,0){3}} \put(5,5){\oval(8,8)[rb]} \put(9,5){\vector(0,1){4}} \end{picture}\else \setlength{\unitlength}{1.2pt} \begin{picture}(10,10)(2,1) \put(2,1){\line(1,0){3}} \put(5,5){\oval(8,8)[rb]} \put(9,5){\vector(0,1){4}} \end{picture}\fi} \newcommand{\ccdec}{\ifx\@currsize\small \setlength{\unitlength}{1.1pt} \begin{picture}(10,10)(2,1) \put(2,9){\line(1,0){3}} \put(5,5){\oval(8,8)[rt]} \put(9,5){\vector(0,-1){4}} \end{picture}\else \setlength{\unitlength}{1.2pt} \begin{picture}(10,10)(2,1) \put(2,9){\line(1,0){3}} \put(5,5){\oval(8,8)[rt]} \put(9,5){\vector(0,-1){4}} \end{picture}\fi} \newcommand{\cvdec}{\ifx\@currsize\small \setlength{\unitlength}{1.1pt} \begin{picture}(10,10)(1,0) \put(1,8){\line(0,-1){3}} \put(5,5){\oval(8,8)[lb]} \put(5,1){\vector(1,0){4}} \end{picture}\else \setlength{\unitlength}{1.2pt} \begin{picture}(10,10)(1,0) \put(1,8){\line(0,-1){3}} \put(5,5){\oval(8,8)[lb]} \put(5,1){\vector(1,0){4}} \end{picture}\fi} \makeatother %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %====================================================================== \newcommand{\解説印}{\fboxsep=1.3pt\noindent\ovalbox{\bf \,解\,説\,}\hspace{0.5em}} % \newcommand{\解答印}{\fboxsep=1.3pt\noindent\fbox{\bf \,解\,答\,}\hspace{0.5em}} \newcommand{\解答印}{\shadowsize=0.15\shadowsize{\fboxsep=1.3pt\noindent\shadowbox{\bf \,解\,答\,}\hspace{0.5em}}} \newcommand{\別解印}{\fboxsep=1.3pt\noindent\fbox{\bf \,別\,解\,}\hspace{0.5em}} \newcommand{\注意印}{\noindent{\bf [注意]}\hspace{0.5em}} %====================================================================== %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %■ベクトルの矢印の高さを揃える定義 % \overrightarrow の矢印の高さを揃える % \vec, \Vec で定義する %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\vec#1{\overrightarrow{\mathstrut #1}} \def\Vec#1{\overrightarrow{\mathstrut {\rm #1}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %=========================================================== % ■二重根号 %----------------------------------------------------------- \def\tsqrt#1{\textstyle\sqrt{#1}} %=========================================================== %%% 平行 // の記号%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\para{% \setlength{\unitlength}{1pt}% \thinlines % \begin{picture}(10, 12)% \put(1,0){/}% \put(4,0){/}% \end{picture}% }% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %■ 答えを太文字 \newcommand{\kotae}[1]{\mbox{\boldmath$#1$}} % \def\kotae#1{\mbox{\boldmath $#1$}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %=========================================================== % ■枠囲み %----------------------------------------------------------- \newcommand{\枠囲}[1]{\,\fboxsep1pt\fbox{ #1 }\,}% 文章中でも数式中でも使える? % \newcommand{\枠}[1]{\fboxsep1pt\fbox{ #1 }\,} %=========================================================== %=========================================================== % ■≦と≧の定義 %----------------------------------------------------------- \def\le{\leqq} \def\ge{\geqq} \newcommand{\LEQQ}{\leqq} \newcommand{\GEQQ}{\geqq} % \newcommand{\LEQQ}{\mathrel{\mathpalette\gl@align<}} % \newcommand{\GEQQ}{\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}}} % エラーになる。理由はよく解らん。 %=========================================================== %=========================================================== % ■行列 2×2 %----------------------------------------------------------- \newcommand{\matrixTT}[4]{ \begin{pmatrix} #1 & #2 \\ #3 & #4 \end{pmatrix} } %=========================================================== %=========================================================== % ■行列 3×3 %----------------------------------------------------------- \newcommand{\matrixTTT}[9]{ \begin{pmatrix} #1 & #2 & #3\\ #4 & #5 & #6\\ #7 & #8 & #9 \end{pmatrix} } %=========================================================== %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ■ 3*1行列の定義 \newcommand{\matrixthreeone}[3]{ \left(\begin{array}{c} #1\\ #2\\ #3 \end{array}\right) } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %=========================================================== % ■△ABCとか % % 「$\∠{ABC}=\Dfrac12\pi$」のような使い方をするので「$」は定義に含めない % %----------------------------------------------------------- \def\△#1{\triangle{\rm #1}} \def\∠#1{\angle{\rm #1}} %=========================================================== %=========================================================== % ■角括弧 複数行 #1 は横幅%,#2は内容 % %----------------------------------------------------------- \newcommand{\角括弧}[2]{% $% \left[ \begin{tabular}{@{}p{.#1\linewidth}}#2\end{tabular} \right]% $% } %=========================================================== %=========================================================== % ■丸括弧 複数行 #1 は横幅%,#2は内容 %----------------------------------------------------------- \newcommand{\丸括弧}[2]{% $% \left( \begin{tabular}{@{}p{.#1\linewidth}}#2\end{tabular} \right)% $% } %=========================================================== %=========================================================== % ■丸囲み数字 ①とか %----------------------------------------------------------- \newcommand{\tyoMaru}[1]{\mbox{{\normalsize \textcircled{\raisebox{-.25ex}{#1}}}}} %=========================================================== %=========================================================== % ■ 微分 df/dt %----------------------------------------------------------- \newcommand{\dd}[2]{% \dfrac{{\rm d}#1}{{\rm d}#2}% } %=========================================================== %=========================================================== % ■ ∫記号のdisplaystyleマクロ %----------------------------------------------------------- % \newcommand{\dint}{\displaystyle\int}% emathと干渉しないように\defで定義 \def\dint{\displaystyle\int} %=========================================================== %=========================================================== % ■ Σ記号のdisplaystyleマクロ %----------------------------------------------------------- \newcommand{\dsum}{\displaystyle\sum} %=========================================================== %=========================================================== % ■ lim記号のdisplaystyleマクロ %----------------------------------------------------------- \newcommand{\dlim}{\displaystyle\lim} \newcommand{\Dsum}{\sum\limits}% ちっさいΣ %=========================================================== %=========================================================== % ■ nCr マクロ %----------------------------------------------------------- \newcommand{\nCr}[2]{% {}_{#1}\mathrm{C}_{#2}% } %=========================================================== %=========================================================== % ■ローマ数字 (i) (ii) (iii) (iv) (v) (vi) (vii) まで定義 %----------------------------------------------------------- \providecommand{\RMi}{\mbox{(\hspace{.1em}i\hspace{.1em})}} \providecommand{\RMii}{\mbox{(ii)}} \providecommand{\RMiii}{\mbox{(i\hspace{-.1em}i\hspace{-.1em}i)}} \providecommand{\RMiv}{\mbox{(i\hspace{-.1em}v)}} \providecommand{\RMv}{\mbox{(\hspace{.1em}v\hspace{.1em})}} \providecommand{\RMvi}{\mbox{(v\hspace{-.1em}i)}} \providecommand{\RMvii}{\mbox{(\hspace{-.1em}v\hspace{-.1em}i\hspace{-.1em}i)}} %=========================================================== %=========================================================== % ■minipage マクロ % % #1 左幅% #2 左内容 #3 右幅% #4 右内容 % % \ミニ頁{左幅%}{左内容}{右幅%}{右内容} % %----------------------------------------------------------- \providecommand{\ミニ頁}[4]{% % \noindent \begin{minipage}[t]{.#1\linewidth}{\setlength{\parindent}{1\Cwd}% \vspace{0mm}% ← これはない方がいいのかも #2} \end{minipage} \begin{minipage}[t]{.#3\linewidth}{\setlength{\parindent}{1\Cwd} \vspace{0mm} #4} \end{minipage} } % http://www2s.biglobe.ne.jp/~nuts/labo/inti/inti05.html % minipage 環境では、変数 \parindent が 0\Cwd になるために起こる。 % インデントをつけたい minipage の始まり (\begin{minipage} の後)に、 % \setlength{\parindent}{1\Cwd} (これが通常時の値)と書けばよい。 % 私の記憶によれば、breakbox 環境内でも同じことが起こったように思う。 %=========================================================== %=========================================================== % ■点A(t, t^3)とか % #1 は点の名前(「A」とか) % #2 は「(t,\,t^3)」とか「(s,\,t,\,u)」と( )内を全部書く % ()の大きさとか,の後のスペースとか微調整ができるように % %----------------------------------------------------------- \providecommand{\点}[2]{${\rm#1} #2$} %=========================================================== %=========================================================== % ■ 証明終了記号 ■ %----------------------------------------------------------- \newcommand{\■}{{\tiny \text{■}}} %=========================================================== \begin{document} %%%%% ■ 本文開始 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\begin{FRAME}% この間に設問を書く% \usepackage{ custom_suseum} をゆうこうにすること \begin{framed} % %---------------------------------------------------------------- % $xyz$座標空間内に,高さ$k$の直円柱$K$がある. その底面の周$C$は$xy$平面上にあり,円$C$の中心は原点Oで, 半径は$R$である. 直円柱$K$の上底(その周を$C'$とする.)は平面$z=k$上にある. 3点P$(0,\,R,\,0)$,P$'(0,\,R,\,k)$,O$'(0,\,0,\,k)$をとる. 平面$z=k$上において,線分O$'$P$'$上に点Mをとり, 点Mを通り直線O$'$P$'$に垂直な直線と円$C'$との交点をL,Nとする. さらに,$\alpha=\angle$MO$'$L,$\beta=\angle$MPOとする. このとき,3点P,L,Nを通る平面によって直円柱$K$を切断することで できる2つの部分の小さい方の体積$V$は,次で与えれられることを示せ. \[V=R^3\tan\beta\left(\sin\alpha-\Dfrac{1}{3}\sin^3\alpha-\alpha\cos\alpha\right)\] \begin{center} %WinTpicVersion4.28b {\unitlength 0.1in \begin{picture}( 23.3000, 19.5000)( 14.4000,-22.0000) % LINE 1 0 3 0 Black White % 2 2535 1235 3420 760 % \special{pn 13}% \special{pa 2536 1236}% \special{pa 3420 760}% \special{fp}% % LINE 2 0 3 0 Black White % 8 2600 900 2545 1225 2600 900 3415 765 2600 900 3325 1110 3325 1110 3315 1810 % \special{pn 8}% \special{pa 2600 900}% \special{pa 2546 1226}% \special{fp}% \special{pa 2600 900}% \special{pa 3416 766}% \special{fp}% \special{pa 2600 900}% \special{pa 3326 1110}% \special{fp}% \special{pa 3326 1110}% \special{pa 3316 1810}% \special{fp}% % LINE 2 2 3 0 Black White % 2 2960 1010 3310 1795 % \special{pn 8}% \special{pa 2960 1010}% \special{pa 3310 1796}% \special{dt 0.045}% % VECTOR 2 0 3 0 Black White % 2 2600 900 2600 300 % \special{pn 8}% \special{pa 2600 900}% \special{pa 2600 300}% \special{fp}% \special{sh 1}% \special{pa 2600 300}% \special{pa 2580 368}% \special{pa 2600 354}% \special{pa 2620 368}% \special{pa 2600 300}% \special{fp}% % LINE 2 2 3 0 Black White % 2 2060 1870 3435 1180 % \special{pn 8}% \special{pa 2060 1870}% \special{pa 3436 1180}% \special{dt 0.045}% % LINE 2 0 3 0 Black White % 2 2600 1935 2600 2200 % \special{pn 8}% \special{pa 2600 1936}% \special{pa 2600 2200}% \special{fp}% % LINE 2 2 3 0 Black White % 4 2600 1600 3320 1820 2600 1600 1900 1400 % \special{pn 8}% \special{pa 2600 1600}% \special{pa 3320 1820}% \special{dt 0.045}% \special{pa 2600 1600}% \special{pa 1900 1400}% \special{dt 0.045}% % LINE 2 2 3 0 Black White % 2 1876 1394 1668 1334 % \special{pn 8}% \special{pa 1876 1394}% \special{pa 1668 1334}% \special{dt 0.045}% % SPLINE 1 0 3 0 Black White % 4 3316 1808 3094 1812 2546 1230 2546 1230 % \special{pn 13}% \special{pa 3316 1808}% \special{pa 3250 1814}% \special{pa 3186 1818}% \special{pa 3154 1818}% \special{pa 3122 1816}% \special{pa 3092 1812}% \special{pa 3064 1806}% \special{pa 3036 1798}% \special{pa 3008 1788}% \special{pa 2980 1776}% \special{pa 2954 1762}% \special{pa 2906 1730}% \special{pa 2858 1690}% \special{pa 2836 1668}% \special{pa 2792 1620}% \special{pa 2752 1568}% \special{pa 2712 1512}% \special{pa 2674 1452}% \special{pa 2636 1390}% \special{pa 2582 1294}% \special{pa 2564 1260}% \special{pa 2546 1230}% \special{fp}% % SPLINE 1 2 3 0 Black White % 4 3428 760 3496 894 3520 1146 3520 1146 % \special{pn 13}% \special{pn 13}% \special{pa 3428 760}% \special{pa 3435 771}% \special{fp}% \special{pa 3451 797}% \special{pa 3456 809}% \special{fp}% \special{pa 3471 836}% \special{pa 3477 847}% \special{fp}% \special{pa 3489 876}% \special{pa 3493 887}% \special{fp}% \special{pa 3503 917}% \special{pa 3507 929}% \special{fp}% \special{pa 3513 959}% \special{pa 3515 972}% \special{fp}% \special{pa 3518 1003}% \special{pa 3519 1015}% \special{fp}% \special{pa 3520 1046}% \special{pa 3520 1059}% \special{fp}% \special{pa 3522 1090}% \special{pa 3521 1102}% \special{fp}% \special{pa 3520 1133}% \special{pa 3520 1146}% \special{fp}% % SPLINE 1 0 3 0 Black White % 5 3320 1802 3420 1724 3512 1430 3522 1228 3522 1228 % \special{pn 13}% \special{pa 3320 1802}% \special{pa 3348 1784}% \special{pa 3374 1766}% \special{pa 3398 1746}% \special{pa 3422 1724}% \special{pa 3440 1700}% \special{pa 3456 1672}% \special{pa 3470 1644}% \special{pa 3482 1614}% \special{pa 3498 1550}% \special{pa 3504 1516}% \special{pa 3508 1484}% \special{pa 3510 1450}% \special{pa 3514 1416}% \special{pa 3520 1320}% \special{pa 3520 1288}% \special{pa 3522 1258}% \special{pa 3522 1228}% \special{fp}% % VECTOR 2 0 3 0 Black White % 2 3310 1820 3770 1945 % \special{pn 8}% \special{pa 3310 1820}% \special{pa 3770 1946}% \special{fp}% \special{sh 1}% \special{pa 3770 1946}% \special{pa 3712 1908}% \special{pa 3720 1932}% \special{pa 3700 1948}% \special{pa 3770 1946}% \special{fp}% % VECTOR 2 0 3 0 Black White % 2 2055 1870 1480 2160 % \special{pn 8}% \special{pa 2056 1870}% \special{pa 1480 2160}% \special{fp}% \special{sh 1}% \special{pa 1480 2160}% \special{pa 1550 2148}% \special{pa 1528 2136}% \special{pa 1532 2112}% \special{pa 1480 2160}% \special{fp}% % ELLIPSE 1 0 3 0 Black White % 4 2600 1600 3525 1910 1670 1605 3520 1615 % \special{pn 13}% \special{ar 2600 1600 926 310 0.0488741 3.1254650}% % ELLIPSE 1 0 3 0 Black White % 4 2600 900 3522 1228 3522 1228 3522 1228 % \special{pn 13}% \special{ar 2600 900 922 328 0.0000000 6.2831853}% % LINE 2 2 3 0 Black White % 2 2600 900 2600 1900 % \special{pn 8}% \special{pa 2600 900}% \special{pa 2600 1900}% \special{dt 0.045}% % STR 2 0 3 0 Black White % 4 2650 345 2650 395 2 0 0 0 % $z$ \put(26.5000,-3.9500){\makebox(0,0)[lb]{$z$}}% % STR 2 0 3 0 Black White % 4 1440 2025 1440 2075 2 0 0 0 % $x$ \put(14.4000,-20.7500){\makebox(0,0)[lb]{$x$}}% % STR 2 0 3 0 Black White % 4 3700 1820 3700 1870 2 0 0 0 % $y$ \put(37.0000,-18.7000){\makebox(0,0)[lb]{$y$}}% % STR 2 0 3 0 Black White % 4 1695 625 1695 675 2 0 0 0 % $C'$ \put(16.9500,-6.7500){\makebox(0,0)[lb]{$C'$}}% % STR 2 0 3 0 Black White % 4 3455 655 3455 705 2 0 0 0 % N \put(34.5500,-7.0500){\makebox(0,0)[lb]{N}}% % LINE 1 0 3 0 Black White % 2 3525 1615 3525 890 % \special{pn 13}% \special{pa 3526 1616}% \special{pa 3526 890}% \special{fp}% % ELLIPSE 2 2 3 0 Black White % 4 2600 1600 3525 1910 3900 1600 1200 1600 % \special{pn 8}% \special{pn 8}% \special{pa 1676 1600}% \special{pa 1676 1592}% \special{fp}% \special{pa 1684 1559}% \special{pa 1686 1553}% \special{fp}% \special{pa 1702 1527}% \special{pa 1706 1521}% \special{fp}% \special{pa 1728 1498}% \special{pa 1734 1492}% \special{fp}% \special{pa 1759 1472}% \special{pa 1764 1468}% \special{fp}% \special{pa 1793 1449}% \special{pa 1799 1446}% \special{fp}% \special{pa 1829 1430}% \special{pa 1835 1427}% \special{fp}% \special{pa 1867 1411}% \special{pa 1874 1409}% \special{fp}% \special{pa 1906 1396}% \special{pa 1913 1393}% \special{fp}% \special{pa 1947 1381}% \special{pa 1954 1378}% \special{fp}% \special{pa 1988 1368}% \special{pa 1995 1366}% \special{fp}% \special{pa 2028 1356}% \special{pa 2036 1354}% \special{fp}% \special{pa 2070 1346}% \special{pa 2078 1344}% \special{fp}% \special{pa 2113 1337}% \special{pa 2121 1336}% \special{fp}% \special{pa 2155 1328}% \special{pa 2163 1327}% \special{fp}% \special{pa 2199 1322}% \special{pa 2207 1320}% \special{fp}% \special{pa 2242 1314}% \special{pa 2251 1314}% \special{fp}% \special{pa 2287 1309}% \special{pa 2294 1308}% \special{fp}% \special{pa 2331 1304}% \special{pa 2339 1304}% \special{fp}% \special{pa 2375 1300}% \special{pa 2383 1300}% \special{fp}% \special{pa 2419 1296}% \special{pa 2427 1296}% \special{fp}% \special{pa 2464 1294}% \special{pa 2472 1294}% \special{fp}% \special{pa 2509 1292}% \special{pa 2517 1292}% \special{fp}% \special{pa 2554 1290}% \special{pa 2562 1290}% \special{fp}% \special{pa 2599 1290}% \special{pa 2607 1290}% \special{fp}% \special{pa 2644 1290}% \special{pa 2652 1290}% \special{fp}% \special{pa 2689 1292}% \special{pa 2697 1292}% \special{fp}% \special{pa 2734 1294}% \special{pa 2742 1294}% \special{fp}% \special{pa 2779 1296}% \special{pa 2787 1297}% \special{fp}% \special{pa 2824 1300}% \special{pa 2832 1300}% \special{fp}% \special{pa 2868 1304}% \special{pa 2876 1304}% \special{fp}% \special{pa 2912 1308}% \special{pa 2920 1310}% \special{fp}% \special{pa 2956 1314}% \special{pa 2963 1316}% \special{fp}% \special{pa 2999 1321}% \special{pa 3007 1322}% \special{fp}% \special{pa 3042 1328}% \special{pa 3049 1330}% \special{fp}% \special{pa 3084 1336}% \special{pa 3091 1338}% \special{fp}% \special{pa 3126 1346}% \special{pa 3134 1348}% \special{fp}% \special{pa 3168 1356}% \special{pa 3176 1358}% \special{fp}% \special{pa 3211 1367}% \special{pa 3218 1370}% \special{fp}% \special{pa 3251 1380}% \special{pa 3258 1382}% \special{fp}% \special{pa 3291 1394}% \special{pa 3298 1397}% \special{fp}% \special{pa 3330 1410}% \special{pa 3337 1413}% \special{fp}% \special{pa 3368 1428}% \special{pa 3375 1431}% \special{fp}% \special{pa 3405 1447}% \special{pa 3410 1451}% \special{fp}% \special{pa 3436 1468}% \special{pa 3443 1473}% \special{fp}% \special{pa 3468 1493}% \special{pa 3472 1496}% \special{fp}% \special{pa 3493 1519}% \special{pa 3498 1526}% \special{fp}% \special{pa 3514 1554}% \special{pa 3517 1559}% \special{fp}% \special{pa 3526 1592}% \special{pa 3526 1600}% \special{fp}% % LINE 1 0 3 0 Black White % 2 1674 898 1676 1610 % \special{pn 13}% \special{pa 1674 898}% \special{pa 1676 1610}% \special{fp}% % STR 2 0 3 0 Black White % 4 3270 1915 3270 1965 2 0 0 0 % P \put(32.7000,-19.6500){\makebox(0,0)[lb]{P}}% % STR 2 0 3 0 Black White % 4 2485 1730 2485 1780 2 0 0 0 % O \put(24.8500,-17.8000){\makebox(0,0)[lb]{O}}% % STR 2 0 3 0 Black White % 4 2210 2010 2210 2060 2 0 0 0 % $C$ \put(22.1000,-20.6000){\makebox(0,0)[lb]{$C$}}% % STR 2 0 3 0 Black White % 4 2415 860 2415 910 2 0 0 0 % $\mathrm{O}'$ \put(24.1500,-9.1000){\makebox(0,0)[lb]{$\mathrm{O}'$}}% % STR 2 0 3 0 Black White % 4 2445 1130 2445 1180 2 0 0 0 % L \put(24.4500,-11.8000){\makebox(0,0)[lb]{L}}% % STR 2 0 3 0 Black White % 4 2900 910 2900 960 2 0 0 0 % M \put(29.0000,-9.6000){\makebox(0,0)[lb]{M}}% % STR 2 0 3 0 Black White % 4 3300 1015 3300 1065 2 0 0 0 % $\mathrm{P}'$ \put(33.0000,-10.6500){\makebox(0,0)[lb]{$\mathrm{P}'$}}% % CIRCLE 2 0 3 0 Black White % 4 3321 1820 3178 1776 2971 1035 2601 1600 % \special{pn 8}% \special{ar 3322 1820 150 150 3.4381385 4.2929833}% % SPLINE 2 0 3 0 Black White % 4 2580 1030 2685 1010 2775 955 2775 955 % \special{pn 8}% \special{pa 2580 1030}% \special{pa 2644 1022}% \special{pa 2676 1014}% \special{pa 2704 1002}% \special{pa 2732 986}% \special{pa 2758 968}% \special{pa 2776 956}% \special{fp}% % STR 2 0 3 0 Black White % 4 3120 1655 3120 1705 2 0 0 0 % $\beta$ \put(31.2000,-17.0500){\makebox(0,0)[lb]{$\beta$}}% % STR 2 0 3 0 Black White % 4 2695 1015 2695 1065 2 0 0 0 % $\alpha$ \put(26.9500,-10.6500){\makebox(0,0)[lb]{$\alpha$}}% \end{picture}}% \end{center} % %-------------------------------------------------------------- \end{framed} %\end{FRAME} %--- 解答 ------------------------------------------------------------------------ {\footnotesize }% footnotesize %%%%%%% ■ 本文終了 ■ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document}