{"id":70,"date":"2011-11-26T20:55:08","date_gmt":"2011-11-26T11:55:08","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=70"},"modified":"2021-11-04T09:29:49","modified_gmt":"2021-11-04T00:29:49","slug":"htb201102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201102\/","title":{"rendered":"\u4e00\u6a4b\u59272011\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u70b9 O \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(r\\) \u306e\u5186\u5468\u4e0a\u306b, \\(2\\) \u70b9 A , B \u3092 \\(\\angle \\text{AOB} \\lt \\dfrac{\\pi}{2}\\) \u3068\u306a\u308b\u3088\u3046\u306b\u3068\u308a \\(\\theta = \\angle \\text{AOB}\\) \u3068\u304a\u304f.\r\n\u3053\u306e\u5186\u5468\u4e0a\u306b\u70b9 C \u3092, \u7dda\u5206 OC \u304c\u7dda\u5206 AB \u3068\u4ea4\u308f\u308b\u3088\u3046\u306b\u3068\u308a, \u7dda\u5206 AB \u4e0a\u306b\u70b9 D \u3092\u3068\u308b.\r\n\u307e\u305f, \u70b9 P \u306f\u7dda\u5206 OA \u4e0a\u3092, \u70b9 Q \u306f\u7dda\u5206 OB \u4e0a\u3092, \u305d\u308c\u305e\u308c\u52d5\u304f.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\text{CP} +\\text{PQ} +\\text{QC}\\) \u306e\u6700\u5c0f\u5024\u3092 \\(r\\) \u3068 \\(\\theta\\) \u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a = \\text{OD}\\) \u3068\u304a\u304f. \\(\\text{DP} +\\text{PQ} +\\text{QD}\\) \u306e\u6700\u5c0f\u5024\u3092 \\(a\\) \u3068 \\(\\theta\\) \u3067\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u3055\u3089\u306b, \u70b9 D \u304c\u7dda\u5206 AB \u4e0a\u3092\u52d5\u304f\u3068\u304d, \\(\\text{DP} +\\text{PQ} +\\text{QD}\\) \u306e\u6700\u5c0f\u5024\u3092 \\(r\\) \u3068 \\(\\theta\\) \u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    OA , OB \u306b\u3064\u3044\u3066\u70b9 C \u3068\u5bfe\u79f0\u306a\u70b9\u3092\u305d\u308c\u305e\u308c C' , C'' \u3068\u304a\u304f\u3068\r\n\\[\r\n\\text{CP} +\\text{PQ} +\\text{QC} =\\text{C'P} +\\text{PQ} +\\text{QC''} \\geqq \\text{C'C''}\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \u70b9 P , Q \u304c\u7dda\u5206 C'C'' \u4e0a\u306b\u3042\u308b\u3068\u304d.\r\n\\(\\angle \\text{AOC} =\\angle \\text{AOC'}\\) , \\(\\angle \\text{BOC} =\\angle \\text{BOC''}\\) \u306a\u306e\u3067\r\n\\[\r\n\\angle \\text{C'OC''} = 2 \\angle \\text{AOB}\r\n\\]\r\n\\(\\text{OC'} = \\text{OC''} = r\\) \u3088\u308a, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62\u306e\u5e95\u8fba\u3067\r\n\\[\r\n\\underline{2r \\sin \\theta}\r\n\\]\r\n

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

    OA , OB \u306b\u3064\u3044\u3066\u70b9 D \u3068\u5bfe\u79f0\u306a\u70b9\u3092\u305d\u308c\u305e\u308c D' , D'' \u3068\u304a\u3044\u3066, (1)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u308b\u3068, \\(\\text{OD'} = \\text{OD''} = a\\) \u3088\u308a, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62\u306e\u5e95\u8fba\u3067\r\n\\[\r\n\\underline{2a \\sin \\theta}\r\n\\]\r\n

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

    \\(a\\) \u304c\u6700\u5c0f\u306b\u306a\u308b\u3068\u304d\u3092\u8003\u3048\u308c\u3070\u3088\u3044.
    \r\n\u3053\u308c\u306f\u70b9 D \u304c\u7dda\u5206 AB \u306e\u4e2d\u70b9\u3068\u306a\u308b\u3068\u304d\u3067, \u3053\u306e\u3068\u304d\r\n\\[\r\na = r \\cos \\dfrac{\\theta}{2}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\r\n\\[\r\n\\underline{2r \\cos \\dfrac{\\theta}{2} \\sin \\theta}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u70b9 O \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(r\\) \u306e\u5186\u5468\u4e0a\u306b, \\(2\\) \u70b9 A , B \u3092 \\(\\angle \\text{AOB} \\lt \\dfrac{\\pi}{2}\\) \u3068\u306a\u308b\u3088\u3046\u306b\u3068\u308a \\(\\theta = \\angle … \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":[47],"tags":[146,13],"class_list":["post-70","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2011","tag-hitotsubashi","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/70","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=70"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/70\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=70"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=70"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}