問題の解答
検索用コード（LaTeX）
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% 例題A3.2.9：基本的な作図（One More）★
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線分ABが与えられたとき，線分ABを$2:3$に内分する点Pを作図せよ．
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% 例題A3.2.9の解答（One More）★
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点$\mathrm{A}$を通り，直線$\mathrm{AB}$と異なる半直線$l$を引く．
[2]半直線$l$上に，$\mathrm{AC}:\mathrm{CD}=2:3$となるように点$\mathrm{C}$，$\mathrm{D}$をとる．
[3]点$\mathrm{C}$を通り，直線$\mathrm{BD}$に平行な直線を引き，線分$\mathrm{AB}$との交点を$\mathrm{P}$とする．このとき，点$\mathrm{P}$が求める点である．
$\mathrm{BD}\parallel\mathrm{PC}$より，
\[
\mathrm{AP}:\mathrm{PB}=\mathrm{AC}:\mathrm{CD}
\]
よって，点$\mathrm{P}$は線分$\mathrm{AB}$を$2:3$に内分する点である．
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 問題A3.2.9：基本的な作図（One More）★
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
線分ABが与えられたとき，線分ABを$2:3$に内分する点Pを作図せよ．
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 問題A3.2.9の解答（One More）★
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
点$\mathrm{A}$を通り，直線$\mathrm{AB}$と異なる半直線$l$を引く．
[2]半直線$l$上に，$\mathrm{AC}:\mathrm{CD}=2:3$となるように点$\mathrm{C}$，$\mathrm{D}$をとる．
[3]点$\mathrm{C}$を通り，直線$\mathrm{BD}$に平行な直線を引き，線分$\mathrm{AB}$との交点を$\mathrm{P}$とする．このとき，点$\mathrm{P}$が求める点である．
$\mathrm{BD}\parallel\mathrm{PC}$より，
\[
\mathrm{AP}:\mathrm{PB}=\mathrm{AC}:\mathrm{CD}
\]
よって，点$\mathrm{P}$は線分$\mathrm{AB}$を$2:3$に内分する点である．
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