{"id":220,"date":"2011-12-03T00:13:14","date_gmt":"2011-12-02T15:13:14","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=220"},"modified":"2021-11-04T13:12:49","modified_gmt":"2021-11-04T04:12:49","slug":"htb200904","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb200904\/","title":{"rendered":"\u4e00\u6a4b\u59272009\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u4e00\u8fba\u306e\u9577\u3055\u304c \\(2\\) \u306e\u6b63\u4e09\u89d2\u5f62 ABC \u3092\u5e73\u9762\u4e0a\u306b\u304a\u304f.\r\n\u25b3ABC \u3092 \\(1\\) \u3064\u306e\u8fba\u306b\u95a2\u3057\u3066 \\(180^{\\circ}\\) \u6298\u308a\u8fd4\u3059\u3068\u3044\u3046\u64cd\u4f5c\u3092\u7e70\u308a\u8fd4\u3057\u884c\u3046.\r\n\u8fba BC \u306b\u95a2\u3059\u308b\u6298\u308a\u8fd4\u3057\u3092 \\(T _ A\\) , \u8fba CA \u306b\u95a2\u3059\u308b\u6298\u308a\u8fd4\u3057\u3092 \\(T _ B\\) , \u8fba AB \u306b\u95a2\u3059\u308b\u6298\u308a\u8fd4\u3057\u3092 \\(T _ C\\) \u3068\u3059\u308b. \u25b3ABC \u306f, \u6700\u521d \\(3\\) \u70b9 A , B , C \u304c\u305d\u308c\u305e\u308c\u5e73\u9762\u4e0a\u306e \\(3\\) \u70b9 O , B' , C' \u306e\u4e0a\u306b\u7f6e\u304b\u308c\u3066\u3044\u308b\u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(T _ A , T _ C , T _ B , T _ C , T _ A\\) \u306e\u9806\u306b\u6298\u308a\u8fd4\u3057\u64cd\u4f5c\u3092\u65bd\u3057\u305f\u3068\u304d\u306e\u9802\u70b9 A \u306e\u79fb\u308a\u5148\u3092 P \u3068\u3059\u308b. \\(T _ A , T _ C , T _ B , T _ A , T _ C , T _ B , T _ A\\) \u306e\u9806\u306b\u6298\u308a\u8fd4\u3057\u64cd\u4f5c\u3092\u65bd\u3057\u305f\u3068\u304d\u306e\u9802\u70b9 A \u306e\u79fb\u308a\u5148\u3092 Q \u3068\u3059\u308b. \\(\\theta = \\angle \\text{POQ}\\) \u3068\u3059\u308b\u3068\u304d, \\(\\cos \\theta\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u6574\u6570 \\(k , l\\) \u306b\u5bfe\u3057\u3066, \\(\\overrightarrow{\\text{OR}} = 3k \\overrightarrow{\\text{OB'}} +3l \\overrightarrow{\\text{OC'}}\\) \u306b\u3088\u308a\u5b9a\u3081\u3089\u308c\u308b\u70b9 R \u306f, \\(T _ A , T _ B , T _ C\\) \u306e\u6298\u308a\u8fd4\u3057\u64cd\u4f5c\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u306b\u3088\u308a, \u70b9 A \u306e\u79fb\u308a\u5148\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    O \u304c\u539f\u70b9, B' \\(( 2 , 0 )\\) , C' \\(( 1 , \\sqrt{3} )\\) \u3068\u306a\u308b\u3088\u3046\u306b\u5ea7\u6a19\u5e73\u9762\u3092\u3068\u308b.
    \r\nP , Q \u306e\u79fb\u308a\u5148\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308a, P \\(( 6 , 2\\sqrt{3} )\\) , Q \\(( 9 , \\sqrt{3} )\\) \u3068\u306a\u308b.<\/p>\r\n\"hitotsubashi_200904_01\"\r\n

    \u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{\\text{OP}} \\right| & = 4\\sqrt{3} , \\\\\r\n\\left| \\overrightarrow{\\text{OQ}} \\right| & = \\sqrt{9^2+3} =2\\sqrt{21} , \\\\\r\n\\overrightarrow{\\text{OP}} \\cdot \\overrightarrow{\\text{OQ}} & = 6 \\cdot 9 +2\\sqrt{3} \\cdot \\sqrt{3} = 60\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\cos \\theta & = \\dfrac{\\overrightarrow{\\text{OP}} \\cdot \\overrightarrow{\\text{OQ}}}{\\left| \\overrightarrow{\\text{OP}} \\right| \\left| \\overrightarrow{\\text{OQ}} \\right|} \\\\\r\n& = \\dfrac{60}{4\\sqrt{3} \\cdot 2\\sqrt{21}} = \\underline{\\dfrac{5 \\sqrt{7}}{14}}\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\(T _ A , T _ C , T _ B , T _ A , T _ C , T _ B\\) ... [A] \u3068\u64cd\u4f5c\u3092\u884c\u3046\u3068, \u70b9 A \u306e\u79fb\u308a\u5148\u306e\u70b9 D \u306f, \\(\\overrightarrow{\\text{OD}} = 3\\overrightarrow{\\text{OB'}}\\) \u3092\u307f\u305f\u3057, \u25b3ABC \u306e\u5411\u304d\u306f\u59cb\u3081\u3068\u540c\u3058\u3067\u3042\u308b.
    \r\n\\(T _ A , T _ B , T _ C , T _ A , T _ B , T _ C\\) ... [B] \u3068\u64cd\u4f5c\u3092\u884c\u3046\u3068, \u70b9 A \u306e\u79fb\u308a\u5148\u306e\u70b9 E \u306f, \\(\\overrightarrow{\\text{OE}} = 3\\overrightarrow{\\text{OC'}}\\) \u3092\u307f\u305f\u3057, \u25b3ABC \u306e\u5411\u304d\u306f\u59cb\u3081\u3068\u540c\u3058\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, [A] \u3092 \\(k\\) \u56de, [B] \u3092 \\(l\\) \u56de\u884c\u3048\u3070, A \u306f R \u306b\u79fb\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u4e00\u8fba\u306e\u9577\u3055\u304c \\(2\\) \u306e\u6b63\u4e09\u89d2\u5f62 ABC \u3092\u5e73\u9762\u4e0a\u306b\u304a\u304f. \u25b3ABC \u3092 \\(1\\) \u3064\u306e\u8fba\u306b\u95a2\u3057\u3066 \\(180^{\\circ}\\) \u6298\u308a\u8fd4\u3059\u3068\u3044\u3046\u64cd\u4f5c\u3092\u7e70\u308a\u8fd4\u3057\u884c\u3046. \u8fba BC \u306b\u95a2\u3059\u308b\u6298\u308a\u8fd4\u3057\u3092 \\(T _ A\\ … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[45],"tags":[146,15],"class_list":["post-220","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2009","tag-hitotsubashi","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=220"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/220\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}